First order logic stuff.(adsbygoogle = window.adsbygoogle || []).push({});

A lot of things don't seem to be axiomatizable. I have like a few remarks that need explaining if anyone could:

-There is no first order theory whose models are precisely the finite fields of characteristic 2.

-The theory of infinite fields of characteristic 2 has no finite axiomatization

-The class of finite groups cannot be axiomatized.

Seems to be related to completeness. Not sure D:

thanks

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# Axiomatizable things

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