top
The elementary theory of ⟨α;×⟩, where α is an ordinal and × denotes ordinal multiplication, is decidable if and only if . Moreover if and respectively denote the right- and left-hand divisibility relation, we show that Th and Th are decidable for every ordinal ξ. Further related definability results are also presented.
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 -