What is Mathematics: Gödel's Theorem and Around (Edition 2015)

Abstract

Introduction to mathematical logic. Part 2.Textbook for students in mathematical logic and foundations of mathematics. Platonism, Intuition, Formalism. Axiomatic set theory. Around the Continuum Problem. Axiom of Determinacy. Large Cardinal Axioms. Ackermann's Set Theory. First order arithmetic. Hilbert's 10th problem. Incompleteness theorems. Consequences. Connected results: double incompleteness theorem, unsolvability of reasoning, theorem on the size of proofs, diophantine incompleteness, Loeb's theorem, consistent universal statements are provable, Berry's paradox, incompleteness and Chaitin's theorem. Around Ramsey's theorem.

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Karlis Podnieks
University of Latvia

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References found in this work

Introduction to mathematical logic.Elliott Mendelson - 1964 - Princeton, N.J.,: Van Nostrand.
The unreasonable effectiveness of mathematics in the natural sciences.Eugene Wigner - 1960 - Communications in Pure and Applied Mathematics 13:1-14.
Logic and Information.Keith Devlin - 1991 - Cambridge University Press.
Science and method.Henri Poincaré - 1914 - Mineola, N.Y.: Dover Publications. Edited by Francis Maitland.

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