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

• Autorzy: Alexis Bès
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03B25: Decidability of theories and sets of sentences
• 03E10: Ordinal and cardinal numbers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 171
• Numer: 3
• Strony: 197-211

Daty

wydano

2002

Twórcy

autor

Alexis Bès

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

Identyfikatory

DOI

10.4064/fm171-3-1