A new kind of numbers, the Non-Dedekindian Numbers, and the extension to them of the notion of algorithmic randomness
Abstract
Description
A new number system, the set of the non-Dedekindian numbers, is introduced and characterized axiomatically. It is then proved that any hypercontinous hyperreal number system is strictly included in the set of the Non-Dedekindian Numbers. The notion of algorithmic-randomness is then extended to non-Dedekindian numbers. As a particular case, the notion of algorithmic randomness for the particular hyperreal number system of Non-Standard Analysis is explicitly analyzed.
The third version differs from the second version in the correction of some lapses
The third version differs from the second version in the correction of some lapses