My problem is the following. I like to know if

London Ware

London Ware

Answered question

2022-05-08

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.

Answer & Explanation

Carleigh Shaffer

Carleigh Shaffer

Beginner2022-05-09Added 10 answers

It depends exactly how you phrase the question.
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 " x ( p 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.

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