A new kind of numbers, the Non-Dedekindian Numbers, and the extension to them of the notion of algorithmic randomness

Details A new kind of numbers, the Non-Dedekindian Numbers, and the extension to them of the notion of algorithmic randomness A new kind of numbers, the Non-Dedekindian Numbers, and the extension to them of the notion of algorithmic randomness

2006-12-20

arxiv.org/abs/math/0612590v3

Mathematics

General Mathematics

The third version differs from the second version in the correction of some lapses

Scientific paper

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.

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