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Ebbinghaus, Heinz-Dieter

Mathematical Logic - 3rd ed - New York Springer 2021 - ix, 304p. - Graduate Texts in Mathematics 291 .

Includes References (291-292)

I. Introduction
II. Syntax of First-Order Languages
III. Semantics of First-Order Languages
IV. A Sequent Calculus
V. The Completeness Theorem
VI. The Lowenheim-Skolem and the Compactness Theorem
VII. The Scope of First-Order Logic
VIII. Syntactic Interpretations and Normal Forms
IX. Extensions of First-Order Logic
X. Computability and its Limitations
XI. Free Models and Logic Programming
XII. An Algebraic Characterization of Elementary Equivalence
XIII. Lindstrom's Theorems

This textbook introduces first-order logic and its role in the foundations of mathematics by examining fundamental questions. What is a mathematical proof? How can mathematical proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs? In answering these questions, this textbook explores the capabilities and limitations of algorithms and proof methods in mathematics and computer science.

ISBN: 9783030738419 (PB)

Subjects--Topical Terms:
Logic -- Computer Science

Universal Decimal Class. No.: 510.2 / EBB