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From Frege to Gödel : A Source Book in Mathematical Logic, 1879-1931

Jean van Heijenoort, editor
Harvard University Press
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Source Books in the History of the Sciences
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The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries.

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1. Frege (1879). Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought

2. Peano (1889). The principles of arithmetic, presented by a new method

3.Dedekind (1890a). Letter to Keferstein

Burali-Forti (1897 and 1897a). A question on transfinite numbers and On well-ordered classes

4.Cantor (1899). Letter to Dedekind

5.Padoa (1900). Logical introduction to any deductive theory

6,Russell (1902). Letter to Frege

7.Frege (1902). Letter to Russell

8.Hilbert (1904). On the foundations of logic and arithmetic

9.Zermelo (1904). Proof that every set can be well-ordered

10.Richard (1905). The principles of mathematics and the problem of sets

11.König (1905a). On the foundations of set theory and the continuum problem

12.Russell (1908a). Mathematical logic as based on the theory of types

13.Zermelo (1908). A new proof of the possibility of a well-ordering

14.Zermelo (l908a). Investigations in the foundations of set theory I

Whitehead and Russell (1910). Incomplete symbols: Descriptions

15.Wiener (1914). A simplification of the logic of relations

16.Löwenheim (1915). On possibilities in the calculus of relatives

17.Skolem (1920). Logico-combinatorial investigations in the satisfiability or provability of mathematical propositions: A simplified proof of a theorem by L. Löwenheim and generalizations of the 18.theorem

19.Post (1921). Introduction to a general theory of elementary propositions

20.Fraenkel (1922b). The notion "definite" and the independence of the axiom of choice

21.Skolem (1922). Some remarks on axiomatized set theory

22.Skolem (1923). The foundations of elementary arithmetic established by means of the recursive mode of thought, without the use of apparent variables ranging over infinite domains

23.Brouwer (1923b, 1954, and 1954a). On the significance of the principle of excluded middle in mathematics, especially in function theory, Addenda and corrigenda, and Further addenda and corrigenda

von Neumann (1923). On the introduction of transfinite numbers

Schönfinkel (1924). On the building blocks of mathematical logic

filbert (1925). On the infinite

von Neumann (1925). An axiomatization of set theory

Kolmogorov (1925). On the principle of excluded middle

Finsler (1926). Formal proofs and undecidability

Brouwer (1927). On the domains of definition of functions

filbert (1927). The foundations of mathematics

Weyl (1927). Comments on Hilbert's second lecture on the foundations of mathematics

Bernays (1927). Appendix to Hilbert's lecture "The foundations of mathematics"

Brouwer (1927a). Intuitionistic reflections on formalism

Ackermann (1928). On filbert's construction of the real numbers

Skolem (1928). On mathematical logic

Herbrand (1930). Investigations in proof theory: The properties of true propositions

Gödel (l930a). The completeness of the axioms of the functional calculus of logic

Gödel (1930b, 1931, and l931a). Some metamathematical results on completeness and consistency, On formally undecidable propositions of Principia mathematica and related systems I, and On completeness and consistency Herbrand (1931b). On the consistency of arithmetic