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Classical Mathematical Logic The Semantic Foundations of Logic 1st Edition by Richard L Epstein, Lesław W Szczerba ISBN 0691123004 9780691123004

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Classical Mathematical Logic The Semantic Foundations of Logic 1, with corrections Edition Richard L. Epstein Digital Instant Download

Author(s): Richard L. Epstein; Lesław W. Szczerba (Contributor)
ISBN(s): 9780691123004, 0691123004
Edition: 1, with corrections
File Details: PDF, 3.49 MB
Year: 2011
Language: english
SKU: EB-34749970 Category: Tags: ,

Classical Mathematical Logic The Semantic Foundations of Logic 1st Edition by Richard L Epstein, Lesław W Szczerba – Ebook PDF Instant Download/Delivery: 0691123004, 9780691123004
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Product details:

ISBN 10: 0691123004 
ISBN 13: 9780691123004
Author: Richard L Epstein, Lesław W Szczerba

In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations. The book provides detailed explanations of all proofs and the insights behind the proofs, as well as detailed and nontrivial examples and problems. The book has more than 550 exercises. It can be used in advanced undergraduate or graduate courses and for self-study and reference. Classical Mathematical Logic presents a unified treatment of material that until now has been available only by consulting many different books and research articles, written with various notation systems and axiomatizations.

Classical Mathematical Logic The Semantic Foundations of Logic 1st Table of contents:

Chapter 1: Propositional Logic

  • Syntax and Semantics

  • Truth Tables and Logical Connectives

  • Tautologies and Contradictions

  • Logical Equivalence and Implication

  • Normal Forms

Chapter 2: Predicate Logic

  • Quantifiers and Variables

  • Syntax and Semantics of First-Order Logic

  • Structures and Interpretations

  • Logical Consequence and Validity

  • Free and Bound Variables

Chapter 3: Proof Theory

  • Formal Proof Systems

  • Natural Deduction

  • Axiomatic Systems

  • Soundness and Completeness

  • Proof Strategies

Chapter 4: Model Theory

  • Models and Interpretations

  • Satisfaction and Truth in a Structure

  • Elementary Equivalence

  • Compactness and Löwenheim–Skolem Theorems

Chapter 5: Meta-Logical Concepts

  • Consistency and Completeness

  • Decidability and Undecidability

  • Recursive Functions and Computability

  • Gödel’s Incompleteness Theorems

Chapter 6: Extensions of Classical Logic

  • Second-Order Logic

  • Modal Logic

  • Intuitionistic Logic

  • Non-Classical Logics

Chapter 7: Applications of Classical Logic

  • Foundations of Mathematics

  • Formal Semantics

  • Logic in Computer Science

  • Automated Theorem Proving

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Tags: Richard L Epstein, Lesław W Szczerba, Classical Mathematical