A Course in Model TheoryCambridge University Press, 08.03.2012 - 248 Seiten This concise introduction to model theory begins with standard notions and takes the reader through to more advanced topics such as stability, simplicity and Hrushovski constructions. The authors introduce the classic results, as well as more recent developments in this vibrant area of mathematical logic. Concrete mathematical examples are included throughout to make the concepts easier to follow. The book also contains over 200 exercises, many with solutions, making the book a useful resource for graduate students as well as researchers. |
Inhalt
2 | 6 |
QUANTIFIER ELIMINATION | 27 |
2 | 41 |
COUNTABLE MODELS | 47 |
1CATEGORICAL THEORIES | 59 |
stable theories | 67 |
MORLEY RANK | 89 |
SIMPLE THEORIES | 109 |
7 | 150 |
PRIME EXTENSIONS | 157 |
Strongly minimal sets | 165 |
APPENDIX A SET THEORY | 185 |
APPENDIX B FIELDS | 191 |
COMBINATORICS | 205 |
SOLUTIONS TO EXERCISES | 213 |
REFERENCES | 235 |
Häufige Begriffe und Wortgruppen
0-definable a₁ acl(A algebraically closed fields algebraically independent arbitrary assume atomic automorphism b₁ bijection binary tree canonical parameter cardinality choose cl(A coheir complete theory conjugates consistent construction closed contains countable models definable DEFINITION denote disjoint divide elementarily equivalent elementary extension elementary map elementary substructure elements eliminates imaginaries embedded equivalence relation F COROLLARY F LEMMA finite set finite subset finite tuple finitely satisfiable following are equivalent forking extension global type hence implies induction infinite sequence isolated isomorphism L-formula L-structure L(A)-formula Morley degree Morley rank Morley sequence n-tuples n-types No-categorical non-forking extension polynomial pregeometry prime extensions procyclic proof of Theorem Proposition prove pseudo-finite fields quantifier elimination quantifier-free realised saturated saturated model simple theories stable theories stationary strongly minimal strongly minimal formula structure SU-rank totally transcendental theories tree property tuple uncountable unique variables Vaughtian pair