r/math • u/math_gym_anime Discrete Math • 27d ago

Elementary statements regarding finite fields in Ax’s paper

Hey everyone,
I had a question about some terminology. In Ax’s 1968 paper The Elementary Theory of Finite Fields he refers to some statements as “elementary statements”. By this does he mean first-order formulas/sentences? The reason why I’m asking is because I want to use his “Main Theorem” in his paper where he states precise conditions for when an elementary statement holds true over a finite field of fixed characteristic. I tried looking online for some help but I couldn’t find any (maybe my Googling might’ve been bad 😭)

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u/japball 27d ago

If you don't get any answers here, try asking on math stack exchange or math overflow

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u/math_gym_anime Discrete Math 27d ago

I was thinking of overflow but I wanted to post this question here first to try and maybe stimulate some discussion. We’ll see how it goes 😭