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