International Journal of Theoretical Physics

, Volume 42, Issue 2, pp 301-307

First online:

Explicit Finitism

  • András KornaiAffiliated withMetacarta Inc.

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This paper takes the first steps in developing a theory of “explicit finitism” which puts explicit limits on the size of finite objects. We provide motivation in the “physics of computation” sense, survey some of the difficulties and describe the appropriate computing machinery. We introduce the subset J of the real numbers that is the central mathematical object emerging from considerations of explicit finitism, and take the first steps in studying its properties.

explicit finitism physics of computation