Model TheoryElsevier, 12 jun 1990 - 649 pagina's Since the second edition of this book (1977), Model Theory has changed radically, and is now concerned with fields such as classification (or stability) theory, nonstandard analysis, model-theoretic algebra, recursive model theory, abstract model theory, and model theories for a host of nonfirst order logics. Model theoretic methods have also had a major impact on set theory, recursion theory, and proof theory.This new edition has been updated to take account of these changes, while preserving its usefulness as a first textbook in model theory. Whole new sections have been added, as well as new exercises and references. A number of updates, improvements and corrections have been made to the main text. |
Inhoudsopgave
| 1 | |
| 61 | |
Chapter 3 Further modeltheoretic constructions | 136 |
Chapter 4 Ultraproducts | 211 |
Chapter 5 Saturated and special models | 292 |
Chapter 6 More about ultraproducts and generalizations | 384 |
Chapter 7 Selected topics | 482 |
Historical notes | 603 |
| 623 | |
Additional references | 634 |
| 641 | |
| 649 | |
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Veelvoorkomende woorden en zinsdelen
a-complete a-saturated a₁ A₂ assume atomic formulas axiom of constructibility b₁ Boolean algebra c₁ complete extension complete theory consistent constant symbols construction COROLLARY countable language countable model countably incomplete countably saturated model define direct product elementarily equivalent elementary chain elementary embedding elementary extension elementary submodel elements example Exercise existential exists F₁ finite subset following are equivalent hence holds homomorphism Horn sentence induction infinite cardinal infinite model isomorphic Keisler Lemma limit ordinal logic measurable cardinal model complete model of power model theory nonempty nonstandard universe notion omits product sentence proof Proposition Prove Ramsey cardinal real closed fields realizes recursively saturated model reduced product relation symbol satisfies saturated models Section sequence set of formulas set of sentences set theory Skolem Suppose Tarski ultrafilter ultrapower ultraproducts uncountable v₁ val F w₁ whence x₁ y₁
Verwijzingen naar dit boek
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