A timeline of mathematical logic; see also history of logic.
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19th century
 1847 – George Boole proposes symbolic logic in The Mathematical Analysis of Logic, defining what is now called Boolean algebra.
 1854 – George Boole perfects his ideas, with the publication of An Investigation of the Laws of Thought.
 1874 – Georg Cantor proves that the set of all real numbers is uncountably infinite but the set of all real algebraic numbers is countably infinite. His proof does not use his famous diagonal argument, which he published in 1891.
 1895 – Georg Cantor publishes a book about set theory containing the arithmetic of infinite cardinal numbers and the continuum hypothesis.
 1899 – Georg Cantor discovers a contradiction in his set theory.
20th century
 1904  Edward Vermilye Huntington develops the backandforth method to prove Cantor's result that countable dense linear orders (without endpoints) are isomorphic.
 1908 – Ernst Zermelo axiomatizes set theory, thus avoiding Cantor's contradictions.
 1915  Leopold Löwenheim publishes a proof of the (downward) LöwenheimSkolem theorem, implicitly using the axiom of choice.
 1918  C. I. Lewis writes A Survey of Symbolic Logic, introducing the modal logic system later called S3.
 1920  Thoralf Skolem proves the (downward) LöwenheimSkolem theorem using the axiom of choice explicitly.
 1922  Thoralf Skolem proves a weaker version of the LöwenheimSkolem theorem without the axiom of choice.
 1929  Mojzesj Presburger introduces Presburger arithmetic and proving its decidability and completeness.
 1928  Hilbert and Wilhelm Ackermann propose the Entscheidungsproblem: to determine, for a statement of firstorder logic whether it is universally valid (in all models).
 1930  Kurt Gödel proves the completeness and countable compactness of firstorder logic for countable languages.
 1930  Oskar Becker introduces the modal logic systems now called S4 and S5 as variations of Lewis's system.
 1930  Arend Heyting develops an intuitionistic propositional calculus.
 1931 – Kurt Gödel proves his incompleteness theorem which shows that every axiomatic system for mathematics is either incomplete or inconsistent.
 1932  C. I. Lewis and C. H. Langford's Symbolic Logic contains descriptions of the modal logic systems S15.
 1933  Kurt Gödel develops two interpretations of intuitionistic logic in terms of a provability logic, which would become the standard axiomatization of S4.
 1934  Thoralf Skolem constructs a nonstandard model of arithmetic.
 1936  Alonzo Church develops the lambda calculus. Alan Turing introduces the Turing machine model proves the existence of universal Turing machines, and uses these results to settle the Entscheidungsproblem by proving it equivalent to (what is now called) the halting problem.
 1936  Anatoly Maltsev proves the full compactness theorem for firstorder logic, and the "upwards" version of the Löwenheim–Skolem theorem.
 1940 – Kurt Gödel shows that neither the continuum hypothesis nor the axiom of choice can be disproven from the standard axioms of set theory.
 1943  Stephen Kleene introduces the assertion he calls "Church's Thesis" asserting the identity of general recursive functions with effective calculable ones.
 1944  McKinsey and Alfred Tarski study the relationship between topological closure and Boolean closure algebras.
 1944  Emil Leon Post introduces the partial order of the Turing degrees, and also introduces Post's problem: to determine if there are computably enumerable degrees lying in between the degree of computable functions and the degree of the halting problem.
 1947  Andrey Markov Jr. and Emil Post independently prove the undecidability of the word problem for semigroups.
 1948  McKinsey and Alfred Tarski study closure algebras for S4 and intuitionistic logic.
19501999
 1950  Boris Trakhtenbrot proves that validity in all finite models (the finitemodel version of the Entscheidungsproblem) is also undecidable; here validity corresponds to nonhalting, rather than halting as in the usual case.
 1952  Kleene presents "Turing's Thesis", asserting the identity of computability in general with computability by Turing machines, as an equivalent form of Church's Thesis.
 1954  Jerzy Łoś and Robert Lawson Vaught independently proved that a firstorder theory which has only infinite models and is categorical in any infinite cardinal at least equal to the language cardinality is complete. Łoś further conjectures that, in the case where the language is countable, if the theory is categorical in an uncountable cardinal, it is categorical in all uncountable cardinals.
 1955  Jerzy Łoś uses the ultraproduct construction to construct the hyperreals and prove the transfer principle.
 1955  Pyotr Novikov finds a (finitely presented) group whose word problem is undecidable.
 1955  Evertt William Beth develops semantic tableaux.
 1958  William Boone independently proves the undecidability of the uniform word problem for groups.
 1959  Saul Kripke develops a semantics for quantified S5 based on multiple models.
 1959  Stanley Tennenbaum proves that all countable nonstandard models of Peano arithmetic are nonrecursive.
 1960  Ray Solomonoff develops the concept of what would come to be called Kolmogorov complexity as part of his theory of Solomonoff induction.
 1961 – Abraham Robinson creates nonstandard analysis.
 1963 – Paul Cohen uses his technique of forcing to show that neither the continuum hypothesis nor the axiom of choice can be proven from the standard axioms of set theory.
 1963  Saul Kripke extends his possibleworld semantics to normal modal logics.
 1965  Michael D. Morley introduces the beginnings of stable theory in order to prove Morley's categoricity theorem confirming Łoś' conjecture.
 1965  Andrei Kolmogorov independently develops the theory of Kolmogorov complexity and uses it to analyze the concept of randomness.
 1966  Grothendieck proves the AxGrothendieck theorem: any injective polynomial selfmap of algebraic varieties over algebraically closed fields is bijective.
 1968  James Ax independently proves the AxGrothendieck theorem.
 1969  Saharon Shelah introduces the concept of stable and superstable theories.
 1970  Yuri Matiyasevich proves that the existence of solutions to Diophantine equations is undecidable
 1975  Harvey Friedman introduces the Reverse Mathematics program.
See also
 History of logic
 History of mathematics
 Philosophy of mathematics
 Timeline of ancient Greek mathematicians – Timeline and summary of ancient Greek mathematicians and their discoveries
 Timeline of mathematics
References
This page was last edited on 17 November 2023, at 18:00