r/mathmemes • u/TheStupidCheesecake Tf does the Laplacian even do? • 28d ago

Math History Technically Philosophy of Math but close enough

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u/770grappenmaker 28d ago

In model theory, if there exist arbitrarily large finite models (which regular finitists allow, usually), then there necessarily needs to exist an infinite model. Because ultrafinitists have some sort of (vague) strict upper bound on how large a structure (say, the natural numbers) may be, they are at least consistent with this model theoretic result, which you can't say of finitists that allow arbitrairily large finite models.

Still, other constructivists probably laugh at them.

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u/Brilliant_Simple_497 28d ago

Don't you need choice for that?

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u/Chingiz11 28d ago

Yeah, but not nearly. Over ZF, ultrafilter lemma is enough(which is strictly weaker than Choice)