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

Volume 171 / 2002

Alexis Bès Fundamenta Mathematicae 171 (2002), 197-211 MSC: 03E10, 03B25. DOI: 10.4064/fm171-3-1


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.


  • Alexis BèsLACL, Département d'Informatique
    Faculté des Sciences et Technologie
    61 avenue du Général de Gaulle
    94010 Créteil Cedex, France

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