000			01589 a2200217 4500
999			_c54498 _d54498
008			210325b ||||| |||| 00| 0 eng d
020			_a9780521518123
082			_a511.34 _bVAA
100			_aVaananen, Jouko
245			_aModels and games
260			_bCambridge University Press, _c2011. _aCambridge:
300			_aix,367 p. : ill. ; _bhb, _c24 cm.
365			_aGBP _b57.99
440			_aCambridge studies in advanced mathematics ; 132
504			_aIncludes bibliographical references (pages 353-361) and index.
520			_aThis gentle introduction to logic and model theory is based on a systematic use of three important games in logic: the semantic game; the Ehrenfeucht–Fraïssé game; and the model existence game. The third game has not been isolated in the literature before but it underlies the concepts of Beth tableaux and consistency properties. Jouko Väänänen shows that these games are closely related and in turn govern the three interrelated concepts of logic: truth, elementary equivalence and proof. All three methods are developed not only for first order logic but also for infinitary logic and generalized quantifiers. Along the way, the author also proves completeness theorems for many logics, including the cofinality quantifier logic of Shelah, a fully compact extension of first order logic. With over 500 exercises this book is ideal for graduate courses, covering the basic material as well as more advanced applications.
650			_aModel theory
650			_aGeneral principles of mathematics
650			_aMathematics
942			_2ddc _cTD