Upward Morley's theorem downward

作者:Sagi Gabor*; Gyenis Zalan
来源:Mathematical Logic Quarterly, 2013, 59(4-5): 303-331.
DOI:10.1002/malq.201110048

摘要

By a celebrated theorem of Morley, a theory T is (1)-categorical if and only if it is -categorical for all uncountable . 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 (1)-categorical T have at most one n-element model for each natural number n (counting up to isomorphism, of course).

  • 出版日期2013-8