Upward Morley's theorem downward
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 (counting up to isomorphism, of course).
categoricity finite models ultraproducts 03c35 03c13 03c20