On Decidability Properties of Local Sentences

Local (first order) sentences, introduced by Ressayre, enjoy very nice decidability properties, following from some stretching theorems stating some remarkable links between the finite and the infinite model theory of these sentences [Res88]. Another stretching theorem of Finkel and Ressayre implies that one can decide, for a given local sentence ϕ and an ordinal α < ωω, whether ϕ has a model of order type α. This result is very similar to B¨uchi’s one who proved that the monadic second order theory of the structure (α, <), for a countable ordinal α, is decidable. It is in fact an extension of that result, as shown in [Fin01] by considering the expressive power of monadic sentences and of local sentences over languages of words of length α. The aim of this paper is twofold. We wish first to attract the reader’s attention on these powerful decidability results proved using methods of model theory and which should find some applications in computer science and w...

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Olivier Finkel
• Keywords: CORR 2007, Education, Local Sentences, Model, Order Type