Strong initial segments of models of IΔ₀

Paola D'Aquino, and Julia F. Knight. "Strong initial segments of models of IΔ₀." Fundamenta Mathematicae 195.2 (2007): 155-176. <http://eudml.org/doc/282883>.

@article{PaolaDAquino2007,
abstract = {McAloon showed that if 𝓐 is a nonstandard model of IΔ₀, then some initial segment of 𝓐 is a nonstandard model of PA. Sommer and D'Aquino characterized, in terms of the Wainer functions, the elements that can belong to such an initial segment. The characterization used work of Ketonen and Solovay, and Paris. Here we give conditions on a model 𝓐 of IΔ₀ guaranteeing that there is an n-elementary initial segment that is a nonstandard model of PA. We also characterize the elements that can be included.},
author = {Paola D'Aquino, Julia F. Knight},
journal = {Fundamenta Mathematicae},
keywords = {nonstandard model; Peano arithmetic; Ramsey theory; largeness},
language = {eng},
number = {2},
pages = {155-176},
title = {Strong initial segments of models of IΔ₀},
url = {http://eudml.org/doc/282883},
volume = {195},
year = {2007},
}

TY - JOUR
AU - Paola D'Aquino
AU - Julia F. Knight
TI - Strong initial segments of models of IΔ₀
JO - Fundamenta Mathematicae
PY - 2007
VL - 195
IS - 2
SP - 155
EP - 176
AB - McAloon showed that if 𝓐 is a nonstandard model of IΔ₀, then some initial segment of 𝓐 is a nonstandard model of PA. Sommer and D'Aquino characterized, in terms of the Wainer functions, the elements that can belong to such an initial segment. The characterization used work of Ketonen and Solovay, and Paris. Here we give conditions on a model 𝓐 of IΔ₀ guaranteeing that there is an n-elementary initial segment that is a nonstandard model of PA. We also characterize the elements that can be included.
LA - eng
KW - nonstandard model; Peano arithmetic; Ramsey theory; largeness
UR - http://eudml.org/doc/282883
ER -