satsifiability however also several direct semantic proofs compactness theorem corollary ie contrapositive compactness theorem says every unsatisfiable first order theory finite unsatisfiable subset theorem central importance model theory words compactness commonplace another cornerstone first order model theory l wenheim skolem theorem according l wenheim skolem theorem every infinite structure countable signature countable elementary substructure conversely infinite cardinal every infinite structure countable signature cardinality less
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