Lectures on mathematical logic: 1 Set theoretical logic - the algebra of models
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
Gordon & Breach
2000
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 282 S. graph. Darst. |
| ISBN: | 905699266X |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface ix
Introduction 1
0. Prerequisites on Sets and Orders 7
1. Sets and Functions 7
2. Well Founded Recursion 11
3. Trees 15
1. Lattices and Boolean Algebras 19
2. Algebras, Homomorphisms and Subalgebras 26
1. Homomorphisms 27
2. Subalgebras 29
3. Quotient Algebras 33
4. Products 36
3. Separation Theorems for Boolean Algebras 40
4. Filters, Ideals, and more on (PI^) 48
5. Term Algebras 55
Realization 0: Unique Readability through Ordered Pairs .... 60
Realization 1: Terms as Numbers I 61
Realization 2: Terms as Trees 61
Realization 3: Terms as Sequences of Characters without
Parentheses 63
Realization 4: Terms as Sequences of Characters with
Parentheses . . 67
Realization 5: Terms as Numbers II 69
Realization 6: Terms as Numbers III 69
Cardinality Questions 70
6. The Logic of Equations 73
Appendix: The Word Problem for Free Lattices 81
7. Free Algebras and Equational Classes 88
8. Equational Equivalences and Clones 98
1. Equational Equivalences 99
2. Clones of Operations 101
9. Polynomials and Normal Forms 114
1. The Algebras L(B,n) of Boolean Polynomials 114
2. Normal Forms in Boolean Algebras 118
Appendix: Normal Forms in Distributive Lattices 120
v
vi Contents
10. Classical Prepositional Logic 126
1. Propositional Logic and Boolean Algebras 128
2. Another Proof of the Finiteness Theorems 131
3. Compactness 135
4. Normal Forms 136
5. A First Glance at Propositional Calculi 142
11. Open Predicate Logic 149
1. Osubstructures and Quotient Structures 153
2. Open Equality Logic 154
12. Quantifier Logic: Languages and Structures 159
1. Evaluation 159
2. Boolean Valued Structures 162
3. Variables Free in a Formula 163
4. Cardinality Questions 165
5. Sublanguages and Reducts 165
6. Substructures 166
7. Morphisms 168
8. Retracts and Protracts 169
9. Equality Logic 169
10. Constant Terms and Diagrams 170
11. Extensions by Constants 172
13. Substitution 175
1. The Replacement Map rep 175
2. Chains and Branches of a Formula 176
3. Replacements Free for a Formula 178
4. Commutativity of Replacement and Evaluation 180
5. The Renaming Map tot 182
6. The Substitution Map sub 186
7. Commuting Replacements 187
8. ResolvingReplacementsintoSuccessiveSingular Replacements 192
14. Henkin Constants, Skolem Functions, and Normal Forms 196
1. Henkin Constants and Henkin Extensions 196
2. The Finiteness Theorems 200
3. Skolem Functions and Skolem Extensions 204
4. Prenex, Skolem and Herbrand Normal Forms 208
5. The Relational Skolem Normal Form 211
15. Algorithms for Consequence 215
1. The Galois Correspondence for Sets of Formulas 216
2. The Galofs Correspondence for Sets of Equations of Formulas 217
3. Boolean Valued Quantifier Logic 219
4. Reduction of 2 Valued to Boolean Valued Quantifier Logic . 225
5. The Consequence cs 229
6. Conclusion 234
Contents vii
16. Lowenheim Skolem Theorems 237
1. Example: Finiteness 239
2. Example: Fragments of Arithmetic 240
3. Models of Set Theory 251
17. Elementary Classes 255
1. Languages with Large Sets of Variables 255
2. Morphisms, Substructures, Morphic Images and Products . . 258
3. The Elementary Classes ModB(M) of B valued Structures . 263
4. The Elementary Classes Mod(C) of 2 valued Structures . . 265
5. Ultraproducts 267
6. Truth Sets, Canonical Structures and Ultraproducts 270
Index of concepts and names 277
Index of symbolic notations 283
Dependences
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| spelling | Felscher, Walter Verfasser aut Lectures on mathematical logic 1 Set theoretical logic - the algebra of models Walter Felscher Amsterdam Gordon & Breach 2000 X, 282 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematische Logik (DE-588)4037951-6 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Mathematische Logik (DE-588)4037951-6 s DE-604 (DE-604)BV012947413 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008816343&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Felscher, Walter Lectures on mathematical logic Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4151278-9 |
| title | Lectures on mathematical logic |
| title_auth | Lectures on mathematical logic |
| title_exact_search | Lectures on mathematical logic |
| title_full | Lectures on mathematical logic 1 Set theoretical logic - the algebra of models Walter Felscher |
| title_fullStr | Lectures on mathematical logic 1 Set theoretical logic - the algebra of models Walter Felscher |
| title_full_unstemmed | Lectures on mathematical logic 1 Set theoretical logic - the algebra of models Walter Felscher |
| title_short | Lectures on mathematical logic |
| title_sort | lectures on mathematical logic set theoretical logic the algebra of models |
| topic | Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Mathematische Logik Einführung |
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