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Recursion Theory for Metamathematics
This work is a sequel to the author's Gödel's Incompleteness Theorems, though it can be read independently by anyone familiar with Gödel's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.
Metamathematics of First-Order Arithmetic
A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.
Metamathematics, Machines and Gödel's Proof
Describes the use of computer programs to check several proofs in the foundations of mathematics.
Recursive Functions and Metamathematics
Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography. Readership: Scholars and advanced students of logic, mathematics, philosophy of science.
The Metamathematics of Algebraic Systems
The Metamathematics of Algebraic Systems
Recursive Functions and Metamathematics
Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.
Metamathematics of Fuzzy Logic
This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. It aims to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named ‘fuzzy inference’ can be naturally understood as logical deduction. It is for mathematicians, logicians, computer scientists, specialists in artificial intelligence and knowledge engineering, and developers of fuzzy logic.
