The pair (ₙ,₀) may fail ₀--compactness

الأصل · EN

Let P be a distinguished unary predicate and K= M: M a model of cardinality alephₙ with Pᵐ of cardinality aleph₀. We prove that consistently for n=4, for some countable first order theory T we have: T has no model in K whereas every finite subset of T has a model in K. We then show how we prove it also for n=2, too.