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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121230A 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 lapsesGeneral MathematicsA new kind of numbers, the Non-Dedekindian Numbers, and the extension to them of the notion of algorithmic randomnesstext