Definable sets in generic structures and their cardinalities

Definable sets in generic structures and their cardinalities Full article

Journal

Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126

Output data

Year: 2018, Volume: 28, Number: 1, Pages: 39-52 Pages count : 18 DOI: 10.3103/S1055134418010030

Tags

calculus for definable sets; cardinality of set; definable set; generative class; generic structure

Authors

Kiouvrekis Y. ¹ , Stefaneas P. ¹ , Sudoplatov S.V. ^2,3,4,5

Affiliations

1	National Technical University of Athens
2	Sobolev Institute of Mathematics
3	Novosibirsk State University
4	Novosibirsk State Technical University
5	Institute of Mathematics and Mathematical Modeling, Almaty

Analyzing diagrams forming generative classes, we describe definable sets and their links in generic structures as well as cardinality bounds for these definable sets, finite or infinite. Introducing basic characteristics for definable sets in generic structures, we compare them each others and with cardinalities of these sets.We introduce calculi for (type-)definable sets allowing to compare their cardinalities. In terms of these calculi, Trichotomy Theorem for possibilities comparing cardinalities of definable sets is proved. Using these calculi, we characterize the possibility to construct a generic structure of a given generative class.

Kiouvrekis Y. , Stefaneas P. , Sudoplatov S.V.
Definable sets in generic structures and their cardinalities
Siberian Advances in Mathematics. 2018. V.28. N1. P.39-52. DOI: 10.3103/S1055134418010030 Scopus РИНЦ OpenAlex

Киуврекис Я.С. , Стефанеас П. , Судоплатов С.В.
Определимые множества в генерических структурах и их мощности
Математические труды. 2017. Т.20. №2. С.52-79. DOI: 10.17377/mattrudy.2017.20.203 РИНЦ

Submitted:	Feb 1, 2017
Published print:	Mar 8, 2018
Published online:	Mar 8, 2018

Scopus:	2-s2.0-85043504428
Elibrary:	35491793
OpenAlex:	W2791726316

DB	Citing
Scopus	3
Elibrary	4
OpenAlex	4