Decidability and definability results related to the elementary theory of ordinal multiplication

Alexis Bès. "Decidability and definability results related to the elementary theory of ordinal multiplication." Fundamenta Mathematicae 171.3 (2002): 197-211. <http://eudml.org/doc/286385>.

@article{AlexisBès2002,
abstract = {The elementary theory of ⟨α;×⟩, where α is an ordinal and × denotes ordinal multiplication, is decidable if and only if $α < ω^\{ω\}$. Moreover if $|_\{r\}$ and $|_\{l\}$ respectively denote the right- and left-hand divisibility relation, we show that Th $⟨ω^\{ω^\{ξ\}\};|_\{r\}⟩$ and Th $⟨ω^\{ξ\};|_\{l\}⟩$ are decidable for every ordinal ξ. Further related definability results are also presented.},
author = {Alexis Bès},
journal = {Fundamenta Mathematicae},
keywords = {decidability of ordinal multiplication},
language = {eng},
number = {3},
pages = {197-211},
title = {Decidability and definability results related to the elementary theory of ordinal multiplication},
url = {http://eudml.org/doc/286385},
volume = {171},
year = {2002},
}

TY - JOUR
AU - Alexis Bès
TI - Decidability and definability results related to the elementary theory of ordinal multiplication
JO - Fundamenta Mathematicae
PY - 2002
VL - 171
IS - 3
SP - 197
EP - 211
AB - The elementary theory of ⟨α;×⟩, where α is an ordinal and × denotes ordinal multiplication, is decidable if and only if $α < ω^{ω}$. Moreover if $|_{r}$ and $|_{l}$ respectively denote the right- and left-hand divisibility relation, we show that Th $⟨ω^{ω^{ξ}};|_{r}⟩$ and Th $⟨ω^{ξ};|_{l}⟩$ are decidable for every ordinal ξ. Further related definability results are also presented.
LA - eng
KW - decidability of ordinal multiplication
UR - http://eudml.org/doc/286385
ER -