The Structure of Models of Peano Arithmetic
Roman Kossak and James Schmerl
Abstract
This book gives an account of the present state of research on lattices of elementary substructures and automorphisms of nonstandard models of arithmetic. Major representation theorems are proved, and the important particular case of countable recursively saturated models is discussed in detail. All necessary technical tools are developed. The list includes: constructions of elementary simple extensions; a partial classification of arithmetic types, in particular Gaifman's theory of definable types; forcing in arithmetic; elements of the Kirby-Paris combinatorial theory of cuts; Lascar's gener ... More
Keywords: nonstandard models, countable recursively saturated models, Gaifman's theory, Kirby-Paris, Lascar's generic automorphisms, Ramsey's theorem
Bibliographic Information
| Print publication date: 2006 | Print ISBN-13: 9780198568278 |
| Published to Oxford Scholarship Online: September 2007 | DOI:10.1093/acprof:oso/9780198568278.001.0001 |
