Upward Morley's theorem downward

Authors

  • Gábor Sági,

    1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15, Budapest, Hungary
    2. Matematika Intézet, Budapesti Műszaki és Gazdaságtudomnyi Egyetem, Pf. 91, Budapest, Hungary
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  • Zalán Gyenis

    1. Department of Mathematics and its Applications, Central European University, Nador u. 9, Budapest, Hungary
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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 inline image (counting up to isomorphism, of course).

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