@MISC{Andreev05atheory, author = {P. V. Andreev and E. I. Gordon}, title = {A Theory of Hyperfinite Sets }, year = {2005} }

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Abstract

We develop an axiomatic set theory — the Theory of Hyperfinite Sets THS, which is based on the idea of existence of proper subclasses of big finite sets. We demonstrate how theorems of classical continuous mathematics can be transfered to THS, prove consistency of THS and present some applications.