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

Alexis Bès

Alexis Bès

Fundamenta Mathematicae, Tome 173 (2002), p. 197-211 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Publié le : 2002-01-01

Zbl 0998.03005

EUDML-ID : urn:eudml:doc:286385

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     title = {Decidability and definability results related to the elementary theory of ordinal multiplication},
     journal = {Fundamenta Mathematicae},
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     year = {2002},
     pages = {197-211},
     zbl = {0998.03005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm171-3-1}
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Alexis Bès. Decidability and definability results related to the elementary theory of ordinal multiplication. Fundamenta Mathematicae, Tome 173 (2002) pp. 197-211. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm171-3-1/