Set Theory and Foundations of Mathematics Volume II Foundations of Mathematics azw3 网盘 高速 下载地址大全 免费

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Contents Preface About the Authors Introduction Propositional Logic Basic Definitions Truth Interpretations The Disjunctive Normal Form Theorem The Deductive Calculus The Soundness Theorem The Completeness Theorem Completeness, Consistency, and Independence Logical vs. Topological Compactness Predicate Logic The Language of Predicate Logic Structures The Deductive Calculus Soundness Theorem for Predicate Logic Models of Predicate Logic The Completeness Theorem for Predicate Logic 4.2 4.3 4.4 4.5 4.6 5. 5.1 5.2 5.3 5.4 6. 6.1 6.2 6.3 6.4 7. 7.1 7.2 7.3 8. 8.1 8.2 8.3 9. 9.1 9.2 10. 10.1 Compactness Isomorphism and Elementary Equivalence Models, Theories, and Axioms Categoricity and Quantifier Elimination Examples of Theories and Structures Boolean Algebras Properties and Examples of Boolean Algebras The Partial Ordering on a Boolean Algebra Filters and Ideals Ultraproducts Computability Finite State Machines Turing Machines Recursive Functions The Halting Problem Decidable and Undecidable Theories Decidable vs. Undecidable Logical Systems Decidable Theories Gödel’s Incompleteness Theorems Algorithmic Randomness Kolmogorov Complexity Incompressible Strings Kolmogorov Complexity and Incompleteness Nonstandard Numbers Nonstandard Natural Numbers Nonstandard Analysis Foundations of Geometry Axioms of Plane Geometry 10.2 10.3 Non-Euclidean Models Finite Geometries Bibliography Index

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