Mathematical Logic and Formalized Theories
：A Survey of Basic Concepts and Results
( 2 )
Publication subTitle ：A Survey of Basic Concepts and Results
Publication series ：2
Publisher： Elsevier Science
Publication year： 2014
E-ISBN: 9781483257976
P-ISBN(Paperback): 9780720420982
P-ISBN(Hardback): 9780720420982
Subject： O141 (mathematical logic) symbolic logic.
Keyword： 数学
Language： ENG
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Description
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.