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Upward Morley's theorem downward
Author(s) -
Sági Gábor,
Gyenis Zalán
Publication year - 2013
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.201110048
Subject(s) - uncountable set , categorical variable , mathematics , isomorphism (crystallography) , model theory , discrete mathematics , calculus (dental) , pure mathematics , combinatorics , statistics , medicine , chemistry , countable set , dentistry , crystal structure , crystallography
By a celebrated theorem of Morley, a theory T is ℵ 1 ‐categorical if and only if it is κ‐categorical for all uncountable κ. In this paper we are taking the first steps towards extending Morley's categoricity theorem “to the finite”. In more detail, we are presenting conditions, implying that certain finite subsets of certain ℵ 1 ‐categorical T have at most one n ‐element model for each natural number n ∈ ω (counting up to isomorphism, of course).