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This is a follow-up to question Completeness vs Compactness in logicCompleteness vs Compactness in logic 68788. One common theme was that compactness in logic is a purely semantic notion, so should have no need of completeness.

The definition of compactness seems to depend in an irreducible way on the concept of a sentence, which appears to be a syntactic notion. So my question is: Is there any purely semantic definition of a sentence in first-order logic?

This is a follow-up to question Completeness vs Compactness in logic 68788. One common theme was that compactness in logic is a purely semantic notion, so should have no need of completeness.

The definition of compactness seems to depend in an irreducible way on the concept of a sentence, which appears to be a syntactic notion. So my question is: Is there any purely semantic definition of a sentence in first-order logic?

This is a follow-up to question Completeness vs Compactness in logic 68788. One common theme was that compactness in logic is a purely semantic notion, so should have no need of completeness.

The definition of compactness seems to depend in an irreducible way on the concept of a sentence, which appears to be a syntactic notion. So my question is: Is there any purely semantic definition of a sentence in first-order logic?

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François G. Dorais
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David Harris
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Semantic definition of sentence

This is a follow-up to question Completeness vs Compactness in logic 68788. One common theme was that compactness in logic is a purely semantic notion, so should have no need of completeness.

The definition of compactness seems to depend in an irreducible way on the concept of a sentence, which appears to be a syntactic notion. So my question is: Is there any purely semantic definition of a sentence in first-order logic?