TY  - BOOK
AU  - Hodges,Wilfrid
TI  - A shorter model theory
SN  - 0521587131
PY  - 1997///
CY  - New York
PB  - Cambridge University Press
KW  - Model theory
N1  - Includes bibliographical references and indexes; Introduction		vii	(2)
Note on notation		ix	
	1 Naming of parts
		1	(20)
	1.1 Structures
		2	(3)
	1.2 Homomorphisms and substructures
		5	(5)
	1.3 Terms and atomic formulas
		10	(5)
	1.4 Parameters and diagrams
		15	(2)
	1.5 Canonical models
		17	(3)
	Further reading
		20	(1)
	2 Classifying structures
		21	(48)
	2.1 Definable subsets
		22	(8)
	2.2 Definable classes of structures
		30	(7)
	2.3 Some notions from logic
		37	(6)
	2.4 Maps and the formulas they preserve
		43	(5)
	2.5 Classifying maps by formulas
		48	(3)
	2.6 Translations
		51	(8)
	2.7 Quantifier elimination
		59	(9)
	Further reading
		68	(1)
	3 Structures that look alike
		69	(24)
	3.1 Theorems of Skolem
		69	(4)
	3.2 Back-and-forth equivalence
		73	(9)
	3.3 Games for elementary equivalence
		82	(9)
	Further reading
		91	(2)
	4 Interpretations
		93	(31)
	4.1 Automorphisms
		94	(7)
	4.2 Relativisation
		101	(6)
	4.3 Interpreting one structure in another
		107	(6)
	4.4 Imaginary elements
		113	(9)
	Further reading
		122	(2)
	5 The first-order case: compactness
		124	(34)
	5.1 Compactness for first-order logic
		124	(6)
	5.2 Types
		130	(4)
	5.3 Elementary amalgamation
		134	(7)
	5.4 Amalgamation and preservation
		141	(6)
	5.5 Expanding the language
		147	(5)
	5.6 Indiscernibles
		152	(4)
	Further reading
		156	(2)
	6 The countable case
		158	(24)
	6.1 Fraisse's construction
		158	(7)
	6.2 Omitting types
		165	(6)
	6.3 Countable categoricity
		171	(4)
	6.4 w-categorical structures by Fraisse's method
		175	(6)
	Further reading
		181	(1)
	7 The existential case
		182	(28)
	7.1 Existentially closed structures
		183	(5)
	7.2 Constructing e.c. structures
		188	(7)
	7.3 Model-completeness
		195	(6)
	7.4 Quantifier elimination revisited
		201	(7)
	Further reading
		208	(2)
	8 Saturation
		210	(40)
	8.1 The great and the good
		211	(9)
	8.2 Big models exist
		220	(5)
	8.3 Syntactic characterisations
		225	(8)
	8.4 One-cardinal and two-cardinal theorems
		233	(4)
	8.5 Ultraproducts and ultrapowers
		237	(11)
	Further reading
		248	(2)
	9 Structure and categoricity
		250	(48)
	9.1 Ehrenfeucht-Mostowski models
		251	(6)
	9.2 Minimal sets
		257	(7)
	9.3 Totally transcendental structures
		264	(9)
	9.4 Stability
		273	(13)
	9.5 Morley's theorem
		286	(10)
	Further reading
		296	(2)
Index to symbols		298	(2)
Index		300	
ER  -