Upward Morley's theorem downward

Sági, Gábor and Gyenis, Zalán (2013) Upward Morley's theorem downward. MATHEMATICAL LOGIC QUARTERLY, 59 (4-5). pp. 303-331. ISSN 0942-5616

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Abstract

By a celebrated theorem of Morley, a theory T is א1-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 א1-categorical T have at most one n-element model for each natural number n∈ω (counting up to isomorphism, of course). © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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