Simple Theories Book

	Preface
	Acknowledgements
1	Preliminaries	1
1.1	Introduction	1
1.2	Notation and model-theoretic prerequisites	5
1.3	Examples	10
1.4	Bibliographical remarks	13
2	Simplicity	15
2.1	The monster model and imaginaries	15
2.2	Dividing and forking	18
2.3	Simplicity	22
2.4	Morley sequences	27
2.5	The Independence Theorem	30
2.6	Simplicity and independence	36
2.7	Bounded equivalence relations	38
2.8	Types	41
2.9	Stability	47
2.10	Bibliographical remarks	50
3	Hyperimaginaries	51
3.1	Hyperimaginaries	51
3.2	Forking for hyperimaginaries	57
3.3	Canonical bases	62
3.4	Internality and analysability	68
3.5	P-closure and local modularity	74
3.6	Elimination of hyperimaginaries	78
3.7	The Lascar group	84
3.8	Bibliographical remarks	93
4	Groups	95
4.1	Type-definable groups	95
4.2	Relatively definable groups	105
4.3	Hyperdefinable groups	110
4.4	Chain conditions and commensurativity	116
4.5	Stabilizers	121
4.6	Quotient groups and analysability	129
4.7	Generically given groups	133
4.8	Locally modular groups	138
4.9	Bibliographical remarks	145
5	Supersimple Theories	147
5.1	Ranks	147
5.2	Weight and domination	155
5.3	Elimination of hyperimaginaries	161
5.4	Supersimple groups	167
5.5	Type-definable supersimple groups	173
5.6	Supersimple division rings	178
5.7	Bibliographical remarks	186
6	Miscellaneous	187
6.1	Small theories	187
6.1.1	Elimination of hyperimaginaries	189
6.1.2	Locally modular theories	193
6.1.3	Theories with finite coding	195
6.1.4	Lachlan's Conjecture	202
6.2	[omega]-categorical theories	204
6.2.1	An amalgamation construction	205
6.2.2	[omega]-categorical supersimple groups	213
6.2.3	[omega]-categorical CM-trivial theories	221
6.3	Simple expansions of simple theories	225
6.3.1	Amalgamating simple theories	225
6.3.2	Simple theories with an automorphism	233
6.4	Low theories	239
6.5	Bibliographical remarks	242
	Bibliography	245
	Index	257