Karlis Podnieks
University of Latvia
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.
Keywords mathematical logic  foundations of mathematics  axiomatic set theory  Hilbert's 10th problem  incompleteness  unsolvability  first order arithmetic
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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 - Dover Publications.

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