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Institution-independent model theory

Frontcover
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Springer, 2008 - 376 Seiten
A model theory that is independent of any concrete logical system allows a general handling of a large variety of logics. This generality can be achieved by applying the theory of institutions that provides a precise mathematical formulation for the intuitive concept of a logical system.
  

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Inhalt

Introduction
1
Categories
7
22 Limits and Colimits
11
23 Adjunctions
16
24 2categories
18
25 Indexed Categories and Fibrations
20
Institutions
23
32 Examples of institutions
28
86 General Birkhoff Axiomatizability
181
Interpolation
189
91 Semantic interpolation
192
92 Interpolation by Axiomatizability
197
93 Interpolation by Consistency
204
94 CraigRobinson Interpolation
211
95 Borrowing Interpolation
215
Definability
222

33 Morphisms and Comorphisms
38
34 Institutions as Functors
45
Theories and Models
48
41 Theories and Presentations
50
42 Theory colimits
57
43 Model Amalgamation
60
44 The method of Diagrams
65
45 Inclusion Systems
74
46 Free Models
82
Internal Logic
91
51 Logical Connectives
92
52 Quantifiers
94
53 Substitutions
97
54 Representable Signature Morphisms
102
55 Satisfaction by Injectivity
107
56 Elementary Homomorphisms
114
Model Ultraproducts
120
62 Fundamental Theorem
124
63 Łoś Institutions
132
64 Compactness
134
65 Finitely Sized Models
137
Saturated Models
141
72 Existence of Saturated Models
144
73 Uniqueness of Saturated Models
152
74 Saturated Ultraproducts
157
Preservation and Axiomatizability
163
82 Axiomatizability by Ultraproducts
168
83 Quasivarieties and Initial Models
170
84 QuasiVariety Theorem
174
85 Birkhoff Variety Theorem
178
101 Explicit implies implicit definability
226
102 Definability by Interpolation
228
103 Definability by Axiomatizability
230
Possible Worlds
235
111 Internal Modal Logic
236
112 Ultraproducts of Kripke models
242
Grothendieck Institutions
252
121 Fibred and Grothendieck Institutions
254
122 Theory Colimits and Model Amalgamation
260
123 Interpolation
267
Institutions with Proofs
275
131 Free Proof Systems
278
132 Compactness
284
133 Prooftheoretic Internal Logic
288
134 The Entailment Institution
297
135 Birkhoff Completeness
302
Specification
317
141 Structured Specifications
318
142 Specifications with Proofs
327
143 Predefined Types
331
Logic Programming
336
151 Herbrand Theorems
338
152 Unification
340
153 Modularization
344
154 Constraints
346
Table of Notation
351
Bibliography
355
Index
368
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