Geodesic
Decidability and definability results related to the elementary theory of ordinal multiplication
Alexis Bès1
1 LACL, Département d'Informatique Faculté des Sciences et Technologie 61 avenue du Général de Gaulle 94010 Créteil Cedex, France
Fundamenta Mathematicae, Tome 171 (2002) no. 3, pp. 197-211.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The elementary theory of $\langle {\alpha ; \times } \rangle $, where $\alpha $ is an ordinal and $\times $ denotes ordinal multiplication, is decidable if and only if $\alpha \omega ^{\omega }$. Moreover if $|_r$ and $|_l$ respectively denote the right- and left-hand divisibility relation, we show that Th $\langle {\omega ^{\omega ^{\xi }}; \mid _r} \rangle $ and Th {$\langle {\omega ^{\xi }; \mid _l} \rangle $ are decidable for every ordinal $\xi $. Further related definability results are also presented.
DOI : 10.4064/fm171-3-1
Keywords: elementary theory langle alpha times rangle where alpha ordinal times denotes ordinal multiplication decidable only alpha omega omega moreover respectively denote right left hand divisibility relation nbsp langle omega omega mid rangle nbsp langle omega mid rangle decidable every ordinal further related definability results presented

Alexis Bès 1

1 LACL, Département d'Informatique Faculté des Sciences et Technologie 61 avenue du Général de Gaulle 94010 Créteil Cedex, France 
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Alexis Bès. Decidability and definability results
 related to the elementary theory of ordinal multiplication. Fundamenta Mathematicae, Tome 171 (2002) no. 3, pp. 197-211. doi : 10.4064/fm171-3-1. http://geodesic.mathdoc.fr/articles/10.4064/fm171-3-1/

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