Alexander Sakharov
 
     

Foundations of Mathematics

- Textbook / Reference -

with contributions by Bhupinder Anand, Harvey Friedman, Haim Gaifman, Vladik Kreinovich, Victor Makarov, Grigori Mints, Karlis Podnieks, Panu Raatikainen, Stephen Simpson,
featured in the Computers/Mathematics section of Science Magazine NetWatch

This is an online resource center for materials that relate to foundations of mathematics (FOM). It is intended to be a textbook for studying the subject and a comprehensive reference. As a result of this encyclopedic focus, materials devoted to advanced research topics are not included. The author has made his best effort to select quality materials on www.

This reference center is organized as a book as opposed to an encyclopedia , dictionary , directory , or link collection . This page represents book's contents page. One can use this page to study the foundations of mathematics by reading topics following the links in their order or jumping over certain chapters. Where appropriate, topics covered in the referred web resource are listed under the link. In particular, it is done if the resource covers more than the respective section heading and title suggest. Presumably, this is the only anchor page one needs to navigate all math foundations topics. I believe you can even save some $$ because the materials listed here should be sufficient, and you do not have to buy a book or two.

The links below are marked in order to indicate the type of material:
   intro - definitions and other introductory material such as entries in online encyclopedias
   more - materials giving a broader coverage of the respective subject
   most - advanced material giving an in-depth coverage of the subject
   topic - supplementary material covering particular topics or particular views of the subject
   quick - quick reference type of material such as lecture slides
Links with similar contents are grouped, and the groups are marked by a vertical bar on the right.

As you know, www links become obsolete pretty quickly. Unfortunately, this especially applies to the kind of materials compiled on this page. For instance, lecture handouts are often removed once the course is finished. Please keep in mind that despite my maintenance efforts, this www reality just kicks in.

Please select link navigation style:
'Frame' leaves the left column in place (default).
'New' opens a new window.
'Jump' replaces the entire window.

What is Foundations of Mathematics?

Foundations of Mathematics - Article from Britannica Concise    intro
Foundations of Mathematics - Article from Wikipedia    intro
What is Foundations of Mathematics? - by Stephen Simpson    intro
  The hierarchy of concepts, mathematics, foundations
What Is a "Foundation" for Mathematics? - by Roger B. Jones    intro
  Branch foundations, fundamental concepts, logical foundations
Foundations of Mathematics: Past, Present, and Future [PS] - by Harvey M. Friedman    more
  FOM and Computer Science, crucial developments in FOM
Mathematical Logic and Foundations - Article from The Mathematical Atlas    intro
  History, applications, subfields of FOM, reference materials, software
Platonism, Intuition and The Nature of Mathematics - by Karlis Podnieks    topic
  Platonism, the mathematical method, axioms, formal theories, Hilbert's program

History

History of the Foundations of Mathematics - by Roger B. Jones    intro
  Greece, axiomatic method, 20-th century schools, logical foundations, etc
A Century of Controversy over the Foundations of Mathematics - Gregory Chaitin's Lecture    more
  Crisis in set theory, paradoxes, Hilbert's formal theories, metamathematic, incompleteness, uncomputability, randomness
Historical notes - from Stephen Wolfram, A New Kind of Science    topic
A History of Set Theory - from School of Mathematical and Computational Sciences, University of St. Andrews    topic
  Cantor, Bolzano, Crelle, Dedekind, Russell, and others
History of Constructivism in The 20th Century - by A.S.Troelstra    more
  Finitism, predicativism and semi-intuitionism, Brouwerian intuitionism, intuitionistic logic, arithmetic, analysis, constructive recursive mathematics, Bishop\u2019s constructivism
See also: Personalities

Hilbert's Program

Hilbert's Program - Article from Stanford Encyclopedia of Philosophy    more
  Finitary point of view, formalism, historical development of Hilbert's program
Partial Realizations of Hilbert's Program - by Stephen G. Simpson    most
  Program explication, reverse mathematics, Q&A
Hilbert's Program Revisited - by Panu Raatikainen    most
  New interpretations of Hilbert's program and recent research relevant to the program

Naive Set Theory

Naive Set Theory - Article from MathWorld    intro
Naive Set Theory - Article from Wikipedia    intro
A Primer on Sets, Classes - Lecture Slides by Stanley N. Burris    quick
  Set membership, equality, subsets, operations on sets, Russell's paradox
Naive Set Theory Is Inconsistent - by Curtis Brown    topic
  Russell's paradox
See also: Paradoxes

Cantor's Diagonal Method

Cantor Diagonal Method - Article from MathWorld    intro
Cantor's Diagonal Argument - Article from Wikipedia    intro

Paradoxes

Paradox - Article from MathWorld    intro

Russell's Paradox

Russell's Antinomy - Article from MathWorld    intro
Russell's Paradox - Article from Stanford Encyclopedia of Philosophy    more
Russell's Paradox - Article from The Internet Encyclopedia of Philosophy    more

Burali-Forti Paradox

Burali-Forti Paradox - Article from MathWorld    intro  
Burali-Forti Paradox - Article from Wikipedia    intro  

Cantor's Paradox

Cantor's Paradox - Article from MathWorld    intro  
Cantor's Paradox - Article from PlanetMath    intro  

Formal Systems

Formal System - from Britannica Concise    intro
The Formalization of Mathematics - by Harvey M. Friedman    more
  Formalization goals, formal set theory, syntax and semantics of formal theories
Formal Languages and Systems - by Heinrich Herre and Peter Schroeder-Heister    more
  Formal language, grammars, deductive systems, logical calculi
Formalized Mathematics - by John Harrison    intro
  History and philosophy, formalization, practical issues

Formal Language

Formal Language - Article from MathWorld    intro
Formal Language - Article from Wikipedia    intro

Axioms and Inference Rules

Axiom - Article from MathWorld    intro
Axiom - Article from Wikipedia    intro
Axiom Schema - Article from MathWorld    intro
Inference Rule - Article from FOLDOC    intro
Syllogism - Article from MathWorld    intro

Axiomatic Method

Axiomatic System - Article from Wikipedia    intro
Axiomatic Method - Article from Britannica Concise    intro
The Axiomatic Method - by Roger B. Jones    intro
The Axiomatic Method - by Anthony Aaby    quick
  Classical logic, Hilbert's formulation, intuitionistic logic

Proof Theory

Proof Theory - Article from Wikipedia    intro
An Introduction to Proof Theory by Samuel R. Buss    most
  Proof theories of propositional logic, first-order logic, intuitionistic logic, linear logic
Highlights in Proof Theory [compressed PS] - by Solomon Feferman    more
  Hilbert's finitary proof theory, Gentzen's L-calculi, countably infinitary methods
Structural Proof Theory [PS] - by Roy Dyckhoff    more
  Natural deduction, sequent calculi
The Foundations of Mathematics - by David Hilbert    topic
  Axioms of logic and arithmetic, discussion of various approaches to formalization of mathematics and its branches
Proof Theory on the eve of Year 2000 - by Solomon Feferman    topic
  Answers to 10 questions about proof theory given by theorists
Proof Interpretations and The Computational Content of Proofs [PS] - by Ulrich Kohlenbach    topic
  Intuitionistic logics, realizability, D-interpretation, negative translation, A-translation
Manipulating Proofs - by Jonathan P. Seldin    quick
  Propositional logic: natural deduction, normalization, sequents, cut elimination
Proof Theory [PS] by Helmut Schwichtenberg    most
  Natural deduction, typed lambda calculus, normalization, computational content of proofs
See also: Natural Deduction and Sequent Calculus

Axiomatizations

Axiomatization - Article from Wikipedia    intro
The Structure of An Axiomatized Theory - by Mary Leng    quick
  Sample axiomatic theories, axioms

Set Theory

Set Theory - Article from Stanford Encyclopedia of Philosophy    more
  The essence and origins of set theory, continuum hypothesis, axiom of choice
Axiomatic Set Theory - by Karlis Podnieks    topic
  Cantor's set theory and its formalization, Zermelo-Fraenkel axioms

Zermelo-Fraenkel Axioms

Zermelo-Fraenkel Axioms - Article from MathWorld    intro  
Zermelo-Fraenkel Axioms - Article from Wikipedia    intro  
Zermelo-Fraenkel Axioms - Article from PlanetMath    intro  
Zermelo-Frankel Set Theory - by Curtis Brown    intro  

Neumann-Bernays-Gödel Set Theory

Von Neumann-Bernays-Gödel Set Theory - Article from MathWorld    intro
Von Neumann-Bernays-Gödel Set Theory - Article from PlanetMath    intro

Continuum Hypothesis

Continuum Hypothesis - Article from MathWorld    intro
Continuum Hypothesis - Article from Wikipedia    intro
Around the Continuum Problem - by Karlis Podnieks    topic
  Counting infinite sets, axioms of constructibility and determinateness, Ackermann's set theory
The Continuum Problem - by Nancy McGough    topic
  Assumptions, style, terminology, mathematics of the continuum
The Continuum Hypothesis - by Hugh Woodin    most

Geometry

Definitions, Axioms, Postulates, Propositions, and Theorems from Euclidean and Non-Euclidean Geometries - by Marvin J. Greenberg    more
  Incidence, betweenness, congruence, continuity, parallelism, hyperbolic geometry

Euclid's Postulates

Euclid's Postulates - Article from MathWorld    intro
Definitions, Postulates & Common Notions - Euclid's Elements - by Robert Campbell    intro

Hilbert's Axioms

Hilbert's Axioms - Article from MathWorld    intro
A Version of Hilbert's axioms for the Euclidean plane - by Ian Chiswell    topic
  Axioms of incidence, betweenness, congruence, parallelism, Dedekind's axiom
Hilbert's Axioms - by Robert Campbell    intro
Parallel Postulate - Article from MathWorld    topic

Non-Euclidean Geometries

Non-Euclidean Geometry - Article from MathWorld    intro
Non-Euclidean Geometry - Article at the web site of University of St. Andrews    more
  Overview of contributions of Bolyai, Lobachevsky, Gauss, Riemann and others

Arithmetic

Peano Axioms - Article from MathWorld    intro
First-Order Proof Theory of Arithmetic - by Samuel R. Buss    most
  Fragments of arithmetic, incompleteness, witnessing theorems
The Dedekind-Peano Number System - Lecture Slides by Stanley N. Burris    quick
Arithmetic - by Stanley N. Burris    more
  First-order arithmetic and Peano arithmetic
First Order Arithmetic - by Karlis Podnieks    topic
  Peano axioms, first-order arithmetic, arithmetic in other formal theories

Other Formal Systems

Algebraic Systems: Group, Ring, Field, Lattice - Articles from MathWorld    intro
A Course in Universal Algebra - by Stanley N. Burris and H.P. Sankappanavar    most
  Lattices, examples of algebras, homomorphisms, varieties, term algebras, free algebras, boolean algebras, connections with model theory
See also: Logic Systems

Mathematical Logic

See also: Axioms and Inference
Classical Logic - Article from Stanford Encyclopedia of Philosophy    more
  Language, deduction, semantics, meta-theory
Introduction to Mathematical Logic - by Vilnis Detlovs and Karlis Podnieks    most
  Propositional and predicate logic, completeness theorems, normal forms, resolution method, unsolvability
A Problem Course in Mathematical Logic - by Stefan Bilaniuk    most
  Propositional logic, first-order logic, computability, incompleteness
A Short Introduction to Logic - by Stefano Berardi    quick
  Propositional and predicate logic, Godel's completeness theorem, strong normalization
Logic - Lecture Notes [PS] - by Josef Schicho    topic
  Formal theories, propositional and predicate logic, the completeness theorem, automatic theorem proving, other predicate theories
Computational Logic - Lecture Handouts by Sergei N. Artemov    quick
  Classical and intuitionistic propositional logic, models, Gentzen proof systems for intuitionistic and modal logic, Kripke completeness theorem, embedding, natural derivations, typed lambda calculus, Curry-Howard isomorphism, combinatory logic

Propositional Calculus

Propositional Calculus - Article from MathWorld    intro
Propositional Logic Terms and Symbols - by Peter Suber    intro
Propositional Logic - Lecture Slides by Stanley N. Burris    quick
Comments on propositional proof systems - by Stanley N. Burris    topic
  Theorem checkers and other algorithms, Frege/Hilbert propositional calculi, Gentzen-style calculi
Deduction Theorem - Article from MathWorld    topic

First-Order Predicate Calculus

First-Order Predicate Calculus - Article from MathWorld    intro
First-Order Predicate Calculus - Article from Wikipedia    intro
First-Order Logic - Lecture Slides by Stanley N. Burris    quick
Logical Laws - by Alex Sakharov    topic
Interpretation - Article from MathWorld    topic
Replacement Theorem - by R. Grandy    topic
Deduction Theorem - Article from MathWorld    intro
See also: Natural Deduction and Sequent Calculus

Normal Forms

Conjunctive Normal Form - Article from MathWorld    intro
Disjunctive Normal Form - Article from MathWorld    intro
Prenex Normal Form - Article from MathWorld    intro
Normal Forms and Skolem Functions - by Anthony Aaby    intro
  Negational normal form, conjunctive normal form, disjunctive normal form, prenex normal form, Skolem normal form

Herbrand Theorem

Herbrand's Theorem - Article from MathWorld    intro
On Herbrand's Theorem - by Samuel R. Buss    most
  Weak and strong forms of the theorem, Herbrand's original version

Intuitionistic Logic

Intuitionistic Logic - Article from MathWorld    intro
Intuitionistic Logic - Article from Wikipedia    intro
Intuitionistic Logic - Article from Stanford Encyclopedia of Philosophy    more
  Intuitionistic first-order predicate logic, Kripke semantics
A Brief Introduction to The Intuitionistic Propositional Calculus - by Stuart A. Kurtz    intro
  Intuitionistic proofs, Curry-Howard isomorphism, semantics
Kripke Semantics [PS] - by Jan Smith    intro
Constructive (Intuitionistic) Logic - by Anthony A. Aaby    quick
  Syntax, Kripke model, analytic tableau
See also: Natural Deduction and Sequent Calculus

Higher-Order Logic

Second-Order Logic and Foundations of Mathematics - by Jouko Vaananen    more
  Informal reasoning, formal languages of the first-order and second-order logics, semantics
Second and Higher-Order Logic - by Robert Harper    intro
  Second-order quantification, second-order predicate logic
Higher Order Logic - by Hans de Nivelle    quick

Modal Logic

Modal Logic - Article from FOLDOC    intro
Modal Logic - by John McCarthy    intro
Modal Logic - Article from Stanford Encyclopedia of Philosophy    more
  Modal logics, deontic Logics, temporal logics, conditional logics and relationships between them, quantifiers in modal logic
Modal Logic - Article by Anthony Aaby    quick
  Syntax, semantics, models

Equational Logic

Equational Logic - Article from MathWorld    intro
Introduction to Equational Logic - by David Gries    intro
Equational Logic - Lecture Slides by Stanley N. Burris    quick
  Terms, semantics, algebras, substitution, unification, term-rewriting systems
Knuth-Bendix Completion Algorithm - Article from MathWorld    topic

Logic Systems

Constructive Logics. Part I: A Tutorial on Proof Systems and Typed lambda-Calculi [PS] - by Jean Gallier    most
  Natural deduction, Gentzen's sequent calculi, calculi transformations, cut elimination
See also: Proof Theory

Natural Deduction

Natural Deduction - Article from FOLDOC    intro
Natural Deduction - by Frank Pfenning    more
  Intuitionistic and classical natural deduction, localizing hypotheses
Natural Deduction: Some Recent Developments - by Jan von Plato    most
  Natural deduction in intuitionistic and classical logics, normalization
Logic - by Helmut Schwichtenberg    more
  Formal languages, natural deduction, normalization, permutative conversions
Natural Deduction for First-Order Logic - by Hans de Nivelle    quick
From Natural Deduction to Sequent Calculus - Slides by Christoph Benzmüller    quick

Sequent Calculus

Sequent Calculus - Article from Wikipedia    intro
Sequent Systems (Gentzen) - by Anthony Aaby    intro
Sequent Calculus Primer - by Alex Sakharov    intro
  Definition, proof theory, sample derivations, formulations, automated deduction
Sequent Calculus - by Frank Pfenning    more
  Relationship between sequent calculus and natural deduction, cut elimination
Sequent Calculi for First-Order Logic - by Hans de Nivelle    quick
Sequent Calculi for First-Order Logic - Slides by Rajeev Gore    quick
Proof Normalization: Gentzen's Hauptsatz - by Amos Omondi    more
  Cut elimination (Hauptsatz), sharpened Hauptsatz, subformula property

Completeness and Consistency

Consistent - Article from PlanetMath    intro
Inconsistent Mathematics - Article from Stanford Encyclopedia of Philosophy    more
Gödel's Completeness Theorem - Article from MathWorld    intro
Gödel's Completeness Theorem - Article from Wikipedia    intro
General Setting for Incompleteness - by Anthony Aaby    topic
  Gödel's and Tarski's theorems, abstract provability system

Gödel's Incompleteness Theorem

Gödel's Incompleteness Theorem - Article from MathWorld    intro
Gödel's Incompleteness Theorem - Article from Wikipedia    intro
Gödel's Incompleteness Theorem - by Dale Myers    intro
  Cantor's power-set theorem, paradoxes, Tarski's undefinability of truth, Godel's two incompleteness theorems
Gödel's Theorems by Peter Smith    most
  Axiomitization of formal theories, arithmetics, recursive functions, Gödel's first and second incompleteness theorems
Incompleteness Theorems - by Karlis Podnieks    topic
  Liar's paradox, self-reference lemma, Godel's two incompleteness theorems
Gödel to Rosser - by Alexander Milowski    topic
  Godel numbers and diagonalization, incompleteness of arithmetic systems

Intuitionism

Intuitionism - Article from Wikipedia    intro
Intuitionism - from Britannica Concise    intro
Lectures on Intuitionism - Historical introduction and Fundamental Notions - by Luitzen Brouwer (Cambridge Lectures on Intuitionism given in 1951)    topic
Gödel's Functional (Dialectica) Interpretation - by Jeremy Avigad and Solomon Feferman    most
  Dialectica interpretation of arithmetic, interpretation of analysis, term model, non-constructive interpretations, interpretation of theories of ordinals
See also: Intuitionistic Logic

Constructive Mathematics

Constructive Mathematics - Article from Stanford Encyclopedia of Philosophy    more
  Constructive interpretation of logic, intuitionistic mathematics, recursive constructive mathematics, Bishop's mathematics, Martin-Lof's type theory
Constructive Mathematics - by Fred Richman    intro
Notes on the Foundations of Constructive Mathematics - by Joan Moschovakis    most
  Background, formal systems and semantics for intuitionistic logic, intuitionistic logic in mathematics
Introduction to Constructive Logic and Mathematics [PS] - by Thomas Streicher    most
  Semantics of constructive logic, embedding, constructive arithmetic and analysis, Kleene's realizability, Kreisel's realizability, higher-type arithmetic, Markov's principle
Relationships between Constructive, Predicative and Classical Systems of Analysis - by Solomon Feferman    more
  Constructive and predicative redevelopments of mathematics, formal systems for Bishop constructive mathematics and for predicativity
Classical and Constructive Logic - by Jeremy Avigad    more
  Classical and constructive viewpoints, number theory and other examples, historical and philosophical issues, symbolic logic, double negation translation, relationship between classical and constructive logic, mathematics, logic and computer science
Constructivism and Proof Theory - by A.S. Troelstra    most
  Intuitionistic logic, its semantics, Heyting arithmetic, constructive mathematics, proof theory of first-order logic and mathematical theories

Model Theory

Model Theory - Article from MathWorld    intro
Model Theory - Article from Wikipedia    intro
Model Theory - Article from Stanford Encyclopedia of Philosophy    more
  Model-theoretic definitions and consequences, expressive strength of languages
First-Order Model Theory - Article from Stanford Encyclopedia of Philosophy    more
  First-order languages, elementary maps, compactness theorem, diagram lemma, Lyndon interpolation theorem, omitting types theorem
Model Theory - by Stephen G. Simpson    most
  Complete theories, compactness theorem, decidability, closed fields, saturated models, quantifier elimination, prime models
Fundamentals of Model Theory - by William Weiss and Cherie D'Mello    most
  Compactness, Löowenheim-Skolem theorems, diagrams, embedding, model completeness, model completions
About Model Theory - by Karlis Podnieks    topic
Models - by Helmut Schwichtenberg    more
  Structures for classical logic, Beth structures for minimal logic, completeness of minumal, intuitionistic, and classical logic, uncountable languages, basics of model theory

Löwenheim-Skolem Theorem

Löwenheim-Skolem Theorem - Article from MathWorld    intro
Löwenheim-Skolem Theorem - Article by Peter Suber    more
  Skolem's paradox, incurable ambiguities

Skolem Paradox

Skolem Paradox - Article from MathWorld    intro

Computability

Introduction to Logic and Recursion Theory - by Edward Boyden, from The Babbage Group web site    intro
  Propositional and first-order logic, completeness and consistency, recursion theory, Post's problem
Computability - by Helmut Schwichtenberg    more
  Register machines, elementary functions, normal form, recursive functions

Computational Models

Turing Machine - Article from MathWorld    intro
Recursive Functions - Article from MathWorld    intro
Markov Algorithms - Article from Wikipedia    intro
The Church-Turing Thesis - Article from MathWorld    intro
The Church-Turing Thesis - Article from Stanford Encyclopedia of Philosophy    more
  Misunderstandings of the thesis, Turing's remarks

Unsolvability

Unsolvability - Article from MathWorld    intro
Godel Number - Article from MathWorld    intro
Enumerability - Article from MathWorld    intro
Creative Sets - Article from MathWorld    topic

Lambda Calculus

Lambda Calculus - Article from Wikipedia    intro
Lambda Calculus and Combinators - by Anthony Aaby    quick
The Lambda-calculus, Combinatory Logic, and Type Systems - by Roger B. Jones    intro
Lambda Tutorial - by Chris Barker    intro

Category Theory

Category Theoretic Perspectives on the Foundations of Mathematics - by Roger B. Jones    intro
Category Theory - from Stanford Encyclopedia of Philosophy    more
  Definitions, history, philosophical significance
Category Theory: The Language of Mathematics - by Elaine Landry    more

Philosophy of Mathematics

Foundations Study Guide: Philosophy of Mathematics - by David S. Ross    intro
  History and overview of logicism, formalism, intuitionism, and objectivism
Logic and Mathematics - by Stephen G. Simpson    intro
  Aristotelian logic, predicate calculus, formal theories
The Modern Development of The Foundations of Mathematics in The Light of Philosophy - by Kurt Gödel (Collected Works, Oxford University Press, 1981)    more
The Philosophy of Mathematics and Hilbert's Proof Theory - by Paul Bernays    most
  Development of math conceptions, math in logic, formal abstraction, infinity, intuitionism, logicism, Hilbert's proof theory
Philosophical Foundations - by Anthony Aaby    quick

General Information

FOM (Foundations of Mathematics) - Automated email list for discussing foundations of mathematics
Proof Theory - email list
Metamath Home Page
  Metamath is a language for expressing theorems and their proofs
Practical Foundations of Mathematics - online book by Paul Taylor    most
  First-order reasoning, types and induction, posets and lattices, Cartesian closed categories, limits and colimits, structural recursion, adjunctions, algebra with dependent types, quantifiers
Foundations of Mathematics - by Stephen Simpson    most
  Computable functions, undecidability of arithmetic, real number system, informal and axiomatic set theory
An Introduction to Mathematical Logic - by Wolfram Pohlers & Thomas Glaß    most
  First-order logic, model theory, decidability, Peano arithmetic, other logics

Reference

Glossary of First-Order Logic - by Peter Suber
Foundations of Mathematics - list of articles from MathWorld
Stanford Encyclopedia of Philosophy - table of contents

Personalities

Georg Cantor - from The MacTutor History of Mathematics archive Georg Cantor - from Wikipedia
David Hilbert - from The MacTutor History of Mathematics archive David Hilbert - from Wikipedia
Kurt Gödel - from The MacTutor History of Mathematics archive The Kurt Gödel Society
Alan Turing - from The MacTutor History of Mathematics archive Alan Turing - from Stanford Encyclopedia of Philosophy
Paul Bernays - from The MacTutor History of Mathematics archive The Bernays Project - This site contains a lot of Bernays works in PDF format. See contents.
John von Neumann - from The MacTutor History of Mathematics archive
Arend Heyting - from The MacTutor History of Mathematics archive
Stephen Kleene - from The MacTutor History of Mathematics archive Stephen Kleene - from Wikipedia
Luitzen Brouwer - from The MacTutor History of Mathematics archive Luitzen Brouwer - from Stanford Encyclopedia of Philosophy
Alonzo Church - from The MacTutor History of Mathematics archive Alonzo Church - from Wikipedia
Bertrand Russell - from The MacTutor History of Mathematics archive Bertrand Russell - from Stanford Encyclopedia of Philosophy
Gerhard Gentzen - from The MacTutor History of Mathematics archive The Collected Works of Gerhard Gentzen - Book summary by Chad E. Brown
Ernst Zermelo - from The MacTutor History of Mathematics archive
Adolf Fraenkel - from The MacTutor History of Mathematics archive
Thoralf Skolem - from The MacTutor History of Mathematics archive
Leopold Löwenheim - from The MacTutor History of Mathematics archive
Emil Post - from The MacTutor History of Mathematics archive
Haskell Curry - from The MacTutor History of Mathematics archive
Andrey Kolmogorov - from The MacTutor History of Mathematics archive
Andrey Markov - from Laboratory of Mathematical Logic of Steklov Institute of Mathematics at St.Petersburg
Alfred Tarski - from The MacTutor History of Mathematics archive
Giuseppe Peano - from The MacTutor History of Mathematics archive
Jacques Herbrand - from The MacTutor History of Mathematics archive

Link Collections

Mathematical Logic Around The World - by Boris Piwinger (University of Bonn, University of Vienna)
Math Topics: Logic/Foundations - from Math Forum @ Drexel
MavicaNET - Logic
Mathematical Logic and Foundations - from MathGuide
Logical Systems - by Peter Suber
Logic - by Denis Roegel
Science > Math > Logic and Foundations - from Open Directory Project (presented by Google)
Science > Mathematics > Foundations of Mathematics - from Yahoo
 

Copyright © 2003 Alexander Sakharov

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