Duality, non-standard elements, and dynamic properties of r.e. sets

Autor:	V. Yu. Shavrukov
Rok vydání:	2016
Předmět:	Discrete mathematics True arithmetic Logic Modulo 010102 general mathematics Duality (mathematics) Disjoint sets 01 natural sciences Prime (order theory) 010101 applied mathematics Wijsbegeerte Order (group theory) Family of sets 0101 mathematics Finite set Mathematics
Zdroj:	Logic Group Preprint Series, 309, 1
ISSN:	0168-0072 0929-0710
DOI:	10.1016/j.apal.2015.10.004
Popis:	We investigate the Priestley dual ( E ⁎ ) ⋆ of the lattice E ⁎ of r.e. sets modulo finite sets. Connections with non-standard elements of r.e. sets in models of 1st order true arithmetic as well as with dynamic properties of r.e. sets are pointed out. Illustrations include the Harrington–Soare dynamic characterization of small subsets, a model-theoretic characterization of promptly simple sets, and relations between the inclusion ordering of prime filters on E ⁎ (a.k.a. points of ( E ⁎ ) ⋆ ) and the complexity of their index sets.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::811be872a3b75444f1143c6132632b09 https://doi.org/10.1016/j.apal.2015.10.004 Zobrazit plný text záznamu Full Text from ScienceDirect