Mathematical Logic A First Course

ISBN-10: 048645018X
ISBN-13: 9780486450186
Edition: 2006
Authors: Joel W. Robbin
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Description: Suitable for advanced undergraduates and graduate students, this self-contained text will appeal to readers from diverse fields and varying backgrounds -- including mathematics, philosophy, linguistics, computer science, and engineering. Topics  More...

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Book details

List price: $14.95
Copyright year: 2006
Publisher: Dover Publications, Incorporated
Publication date: 7/7/2006
Binding: Paperback
Pages: 238
Size: 5.25" wide x 8.50" long x 0.75" tall
Weight: 0.550
Language: English

Suitable for advanced undergraduates and graduate students, this self-contained text will appeal to readers from diverse fields and varying backgrounds -- including mathematics, philosophy, linguistics, computer science, and engineering. Topics include 1st-order recursive arithmetic, 1st- and 2nd-order logic, and the arithmetization of syntax. Numerous exercises; some solutions. 1969 edition.

Preface
Note to the Student
The Propositional Calculus
Formation Rules for P
Formal Semantics of P
Axiomatization of P
The Deduction Theorem
Some Theorem Schemas of P
Completeness
First-Order Logic
Formation Rules for L([characters not reproducible], X)
Free and Bound Variables
Models
Validity
Axiomatization of L([characters not reproducible], X)
Propositional Calculus
The Deduction Theorem
Some Theorems of First-Order Logic
The Soundness Theorem
The Extension Lemma
The Completeness Theorem
First-Order Logic with Equality
First-Order Recursive Arithmetic
Primitive Recursive Functions
Some Primitive Recursive Functions
Formation Rules for RA
Semantics
Axiomatics
Soundness
Sentences without Variables
Arithmetization of Syntax
Finite Sums and Products
Primitive Recursive Relations
Definition by Cases and the Least Number Operator
Prime Numbers
Primitive Recursiveness of the Prime Decomposition
Godel Numbers
Primitive Recursiveness of the Notion of Function Constant
Primitive Recursiveness of the Notion of Term
Primitive Recursiveness of the Notion of Wff
Substitution
Deductions
The Incompleteness Theorems and Other Applications of the Liar Paradox
The First Godel Incompleteness Theorem
Proof of the First Godel Theorem in RA
The Second Godel Incompleteness Theorem
Tarski's Theorem
Arithmetical Sets
Recursive Sets and Decision Procedures
Church's Theorem for RA
Second-Order Logic
Formation Rules for L[subscript 2]([characters not reproducible], X)
Axiomatics for L[subscript 2]([characters not reproducible], X)
Semantics of Second-Order Logic
The Completeness Theorem for Second-Order Logic
Equality
Second-Order Peano Arithmetic
Primitive Recursive Functions
Numeralwise Representability
Godel's Theorem for PA[subscript 2]
Church's Theorem for Second-Order Logic
Categoricity of PA[subscript 2]
Skolem's Paradox
Formal Set Theory
Appendix
Sets and Functions
Induction
Primitive Recursion
Countable Sets
Answers to Selected Exercises
Suggested Reading
Index of Symbols
Index

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