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Mathematical Logic and Formalized Theories : A Survey of Basic Concepts and Results, PDF eBook

Mathematical Logic and Formalized Theories : A Survey of Basic Concepts and Results PDF

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Mathematical Logic and Formalized Theories: A Survey of Basic Concepts and Results focuses on basic concepts and results of mathematical logic and the study of formalized theories. The manuscript first elaborates on sentential logic and first-order predicate logic.

Discussions focus on first-order predicate logic with identity and operation symbols, first-order predicate logic with identity, completeness theorems, elementary theories, deduction theorem, interpretations, truth, and validity, sentential connectives, and tautologies.

The text then tackles second-order predicate logic, as well as second-order theories, theory of definition, and second-order predicate logic F2.

The publication takes a look at natural and real numbers, incompleteness, and the axiomatic set theory.

Topics include paradoxes, recursive functions and relations, Godel's first incompleteness theorem, axiom of choice, metamathematics of R and elementary algebra, and metamathematics of N. The book is a valuable reference for mathematicians and researchers interested in mathematical logic and formalized theories.

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