I need help. My problem is the following. I like to know if there exist a sentence true in complex a field but false in a field of positive characteristic. Thanks
2026-04-01 11:21:18.1775042478
A sentence true in a field of characteristic 0 but false in a field of positive characteristic
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It depends exactly how you phrase the question. (And I presume "sentence" means "first-order sentence", because of the model theory tag.)
If you want a sentence true in every field of characteristic zero, and false in every field of positive characteristic, then this can't happen; consider the negation of such a sentence, and apply the Compactness Theorem.
If you want a sentence true in every field of characteristic zero and false in some field of positive characteristic, consider the sentence "$\forall x(p\cdot x=0)$" for a fixed prime $p$; this is true in exactly the fields of characteristic $p$, so its negation is true in every field of characteristic zero, and false in some field of positive characteristic.