TY - JOUR

T1 - Definable Sets in Generic Structures and their Cardinalities

AU - Kiouvrekis, Y.

AU - Stefaneas, P.

AU - Sudoplatov, S. V.

N1 - Publisher Copyright: © 2018, Allerton Press, Inc.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - calculus for definable sets

KW - cardinality of set

KW - definable set

KW - generative class

KW - generic structure

UR - http://www.scopus.com/inward/record.url?scp=85043504428&partnerID=8YFLogxK

U2 - 10.3103/S1055134418010030

DO - 10.3103/S1055134418010030

M3 - Article

AN - SCOPUS:85043504428

VL - 28

SP - 39

EP - 52

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 1

ER -