000			a
999			_c33768 _d33768
008			250306b xxu||||| |||| 00| 0 eng d
020			_a9783319924137
082			_a511.3 _bMOE
100			_aMoerdijk, Ieke
245			_aSets, models and proofs
260			_bSpringer, _c2018 _aCham :
300			_axiv, 141 p. ; _bill., (b & w), _c24 cm
365			_b32.99 _c€ _d93.20
490			_aSpringer undergraduate mathematics series
504			_aIncludes bibliographical references and index.
520			_aThis textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas. The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzen-style natural deduction and a detailed proof of Gödel’s completeness theorem for first-order logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for self-study, though it is ideally suited as a text for a one-semester university course in the second or third year.
650			_aSymbolic and mathematical
650			_aAxiom of Choice bi
650			_aCompactness Theorem
650			_aContinuum Hypothesis
650			_aFIrst-order logic
650			_aInjective function
650			_aL-formula
650			_aModel Theory
650			_aProof tree
650			_aQuantifier elimination
650			_aSurjective function
650			_aWell-ordered set
700			_aOosten, Jaap van
942			_2ddc _cBK