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I did some research on a style of mathematics in which everything is finite, in which exceedingly large numbers take the place of the infinities of classical and intuitionistic logic.
It uses a logic intermediate between classical and intuitionistic logic.
This page describes some of the philosophy behind it. The research was done some years ago, and in fact I have forgotten most of it, and would need to look it up again if anyone was interested. Reactions to it were unfavourable, so I never tried to publish it. However, I was satisfied with it myself, as it answered the basic question that motivated the research and lead to new areas for research which I enjoyed following up, so could possibly be of interest to others too.
http://www.rcwalker.freeserve.co.uk/robert/largenumbersasinfinite.htm
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