does a consistent closed theory in a finite languge, which is not finitely axiomatizable has an infinite model? i need help to know if this is true or not. and also if it is true can i prove it by compactness?
2026-03-25 01:27:59.1774402079
does a consistent closed theory in a finite languge, which is not finitely axiomatizable has an infinite model?
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Hint: Use compactness to prove that if a theory has arbitrarily large finite models, then it has an infinite model. Now observe that for every finite $n$, there are finitely many structures of size $n$ up to isomorphism (since the language is finite).