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Constructing quasiminimal structures
Author(s) -
Haykazyan Levon
Publication year - 2017
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201600071
Subject(s) - mathematics , outcome (game theory) , order (exchange) , upper and lower bounds , pure mathematics , epistemology , mathematical economics , mathematical analysis , philosophy , finance , economics
Abstract Quasiminimal structures play an important role in non‐elementary categoricity. In this paper we explore possibilities of constructing quasiminimal models of a given first‐order theory. We present several constructions with increasing control of the properties of the outcome using increasingly stronger assumptions on the theory. We also establish an upper bound on the Hanf number of the existence of arbitrarily large quasiminimal models.