ON COHESIVE POWERS OF LINEAR ORDERS

Author:

DIMITROV RUMEN,HARIZANOV VALENTINAORCID,MOROZOV ANDREYORCID,SHAFER PAULORCID,SOSKOVA ALEXANDRA A.ORCID,VATEV STEFAN V.ORCID

Abstract

AbstractCohesive powersof computable structures are effective analogs of ultrapowers, where cohesive sets play the role of ultrafilters. Let$\omega $,$\zeta $, and$\eta $denote the respective order-types of the natural numbers, the integers, and the rationals when thought of as linear orders. We investigate the cohesive powers of computable linear orders, with special emphasis on computable copies of$\omega $. If$\mathcal {L}$is a computable copy of$\omega $that is computably isomorphic to the usual presentation of$\omega $, then every cohesive power of$\mathcal {L}$has order-type$\omega + \zeta \eta $. However, there are computable copies of$\omega $, necessarily not computably isomorphic to the usual presentation, having cohesive powers not elementarily equivalent to$\omega + \zeta \eta $. For example, we show that there is a computable copy of$\omega $with a cohesive power of order-type$\omega + \eta $. Our most general result is that if$X \subseteq \mathbb {N} \setminus \{0\}$is a Boolean combination of$\Sigma _2$sets, thought of as a set of finite order-types, then there is a computable copy of$\omega $with a cohesive power of order-type$\omega + \boldsymbol {\sigma }(X \cup \{\omega + \zeta \eta + \omega ^*\})$, where$\boldsymbol {\sigma }(X \cup \{\omega + \zeta \eta + \omega ^*\})$denotes the shuffle of the order-types inXand the order-type$\omega + \zeta \eta + \omega ^*$. Furthermore, ifXis finite and non-empty, then there is a computable copy of$\omega $with a cohesive power of order-type$\omega + \boldsymbol {\sigma }(X)$.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference24 articles.

1. Cohesive powers of computable structures;Dimitrov;Godishnik na Sofiǐskiya Universitet “Sv. Kliment Ohridski”. Fakultet po Matematika i Informatika. Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique,2009

2. A class of $${\Sigma _{3}^{0}}$$ modular lattices embeddable as principal filters in $${\mathcal{L}^{\ast }(V_{\infty })}$$

3. Computable model theory

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