Models and Ultraproducts: An IntroductionCourier Corporation, 01.01.2006 - 322 Seiten Geared toward first-year graduate students, this text assumes only an acquaintance with the rudiments of set theory to explore homogeneous universal models, saturated structure, extensions of classical first-order logic in terms of generalized quantifiers and infinitary languages, and other topics. Numerous exercises appear throughout the text. 1974 edition. |
Häufige Begriffe und Wortgruppen
algebraically closed fields assume atomic formulas axiom of choice Boolean algebra cardinal oz chain chapter Clearly completeness theorem completes the proof consistent contains COROLLARY countable set definable definition densely ordered domain elementarily equivalent elementary embedding elementary extension enumeration example exercise filter find finite set finite subset fip first order property follows function hence holds ifi ifl immediate consequence infinite cardinal KEISLER language obtained lattice lemma let F limit cardinal Los’s theorem measurable cardinal model complete model of arithmetic model of cardinal natural numbers non-empty non-principal ultrafilter one—one map ordinal predicate calculus propositional calculus provable prove quantifier realization recursively regular cardinal relational structures result sentences of L0 sequence set of sentences set theory structure of cardinal substructure successor cardinal Suppose symbols tautology theorem 3.1 ultrafilter ultrafilter F ultrafilter pair ultralimits ultrapower ultraproducts unary predicate letter uncountable Vaught’s vector space well-ordered