Model Theory : An IntroductionSpringer Science & Business Media, 06.04.2006 - 345 Seiten Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures |
Inhalt
| 1 | |
| 7 | |
Basic Techniques | 33 |
Algebraic Examples | 71 |
Realizing and Omitting Types 115 | 114 |
Indiscernibles | 175 |
ωStable Theories 207 | 206 |
ωStable Groups | 251 |
Geometry of Strongly Minimal Sets | 289 |
A Set Theory 315 | 314 |
B Real Algebra | 323 |
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Häufige Begriffe und Wortgruppen
A C M Abelian group acl(A aclº algebraic group algebraically closed field automorphism axioms C-formula C-theory canonical base claim closure constant symbol constructible contradiction Corollary countable countable language countable models definable sets definable subgroup Definition differential field differentially closed differentially closed fields disjoint element elementary embedding elementary extension equivalence relation example Exercise finite Morley rank finitely satisfiable function symbol homogeneous induction interpret irreducible isolated type isomorphic L-structure Lemma Let F limit ordinal linear order model-complete Morley rank one-based order indiscernibles Peano arithmetic player polynomial prime model Proof Let Proof Suppose Proposition prove quantifier elimination quantifier-free formula real closed field realizes recursive RM(p saturated model semialgebraic sequence of order Show Skolem Stab(p strongly minimal strongly minimal set structure subset uncountable Vaughtian pair w-stable