A Course on Mathematical Logic

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Springer Science & Business Media, Feb 15, 2008 - Mathematics - 150 pages
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This book provides a distinctive, well-motivated introduction to mathematical logic. It starts with the definition of first order languages, proceeds through propositional logic, completeness theorems, and finally the two Incompleteness Theorems of Godel.

 

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Contents

Syntax of FirstOrder Logic
1
12 Terms of a Language
4
13 Formulas of a Language
6
14 FirstOrder Theories
10
Semantics of FirstOrder Languages
15
21 Structures of FirstOrder Languages
16
22 Truth in a Structure
17
23 Model of a Theory
19
Completeness Theorem and Model Theory
65
52 Interpretations in a Theory
70
53 Extension by Definitions
72
54 Compactness Theorem and Applications
74
55 Complete Theories
77
56 Applications in Algebra
79
Recursive Functions and Arithmetization of Theories
82
61 Recursive Functions and Recursive Predicates
84

24 Embeddings and Isomorphisms
20
Propositional Logic
29
31 Syntax of Propositional Logic
30
33 Compactness Theorem for Propositional Logic
33
34 Proof in Propositional Logic
37
35 Metatheorems in Propositional Logic
38
36 Post Tautology Theorem
42
Proof and Metatheorems in FirstOrder Logic
45
42 Metatheorems in FirstOrder Logic
46
43 Some Metatheorems in Arithmetic
59
44 Consistency and Completeness
62
62 Semirecursive Predicates
93
63 Arithmetization of Theories
96
64 Decidable Theories
103
Incompleteness Theorems and Recursion Theory
107
72 First Incompleteness Theorem
115
73 Arithmetical Sets
116
74 Recursive Extensions of Peano Arithemetic
125
75 Second Incompleteness Theorem
131
References
135
Index
137
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