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Mathematical Logic and Formalized Theories

A Survey of Basic Concepts and Results

2nd Edition - January 1, 1971

Author: Robert L. Rogers

Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 5 7 9 7 - 6

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.… Read more

Mathematical Logic and Formalized Theories

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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, Gödel'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.