Another Jump Inversion Theorem for Structures

Autor:	Stefan V. Vatev
Rok vydání:	2013
Předmět:	Discrete mathematics Combinatorics Mathematics::Logic Jump Successor ordinal Countable set Inversion (discrete mathematics) Mathematics
Zdroj:	Lecture Notes in Computer Science ISBN: 9783642390524 CiE
DOI:	10.1007/978-3-642-39053-1_49
Popis:	In this paper we investigate the question of existence of a jump inversion structure for a given structure \(\mathcal{A}\) in the context of their respective degree spectra and the sets definable in them by computable infinitary formulae. More specifically, for a countable structure \(\mathcal{A}\) and a computable successor ordinal α, we show that we can apply the construction from [4] to build a structure \(\mathcal{N}_\alpha\) such that the sets definable in \(\mathcal{A}\) by \(\Sigma^{c,\Delta^0_\alpha}_1\) formulae are exactly the sets definable in \(\mathcal{N}_\alpha\) by \(\Sigma^{c}_{\alpha}\) formulae.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::728ec4cb203966fae91b79339598e9e0 https://doi.org/10.1007/978-3-642-39053-1_49 Zobrazit plný text záznamu