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The Structure of Models of Peano Arithmetic
Aimed at graduate students and research logicians and mathematicians, this much-awaited text covers over forty years of work on relative classification theory for non-standard …
Cardinal Arithmetic
Is the continuum hypothesis still open? If we interpret it as finding the laws of cardinal arithmetic (really exponentiation since addition and multiplication were classically …
Models of Peano Arithmetic
Nonstandard models of arithmetic are of interest to mathematicians through the presence of infinite (or nonstandard) integers and the various properties they inherit from the …
Arithmetic, Proof Theory, and Computational Complexity
This book principally concerns the rapidly growing area of what might be termed "Logical Complexity Theory", the study of bounded arithmetic, propositional proof systems, length of …