We know that different models of the Reals are elementary equivalent but not isomorphic. In the hyperreals, we have that the Archimedean principle does not hold but it does hold in the standard Reals ( i.e., the hyperreals allow for the existence of indefinitely-small and indefinitely -large numbers, but the standard Reals do not; indefinitely-small numbers must equal zero) . Let's make some set-theoretic assumption about cardinalities: is there a standard second-order property that holds for models of fixed cardinality but does not hold for models of lower cardinality, like in the case of the Archimedean principle for the hyperreals and the Reals?(adsbygoogle = window.adsbygoogle || []).push({});

Thanks.

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# Models of the Reals of All Cardinalities and Equivalence

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