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There are models of integers with and without Szmeredi's theorem,In summary: we have Hachel with his dumb "complex numbers", now an inventor of "multiple models of integers". Let's just find some genius of "new real numbers" and we could form a team in the psychiatric hospital :)
it's _independent_ usual laws of small numbers since there are
multiple models of integers, and of course a neat, simple, direct
logical argument that there's no standard model of integers,
only fragments and extensions.
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