Author:
GALEOTTI LORENZO,LÖWE BENEDIKT
Abstract
AbstractThe complete characterisation of order types of non-standard models of Peano arithmetic and its extensions is a famous open problem. In this paper, we consider subtheories of Peano arithmetic (both with and without induction), in particular, theories formulated in proper fragments of the full language of arithmetic. We study the order types of their non-standard models and separate all considered theories via their possible order types. We compare the theories with and without induction and observe that the theories without induction tend to have an algebraic character that allows model constructions by closing a model under the relevant algebraic operations.
Publisher
Cambridge University Press (CUP)
Reference29 articles.
1. Definability and decision problems in arithmetic;Robinson;this Journal,1949
2. Models of PA: when two elements are necessarily order automorphic
3. The automorphism group of a resplendent model
4. [13] Llewellyn-Jones, D. , Presburger arithmetic and pseudo-recursive saturation , Ph.D. thesis, University of Birmingham, 2001.