Alternative algebraic definitions of the Hessenberg natural operations in the ordinal numbers

Konstantinos Constantine Kyritsis (1)

1 TEI - Technological Educational Institute of Epirus

This paper proves prerequisite results for the theory of Ordinal Real Numbers. In this paper, is proved that any field-inherited abelian operations and the Hessenberg operations ,in the ordinal numbers coincide. It is given an algebraic characterisation of the Hessenberg operations ,that can be described as an abelian, well- ordered,double monoid with cancelation laws.

Mots clés: Hessenberg natural operations (in the ordinal numbers); ordinal numbers; semirings; inductive rules; transfinite induction

Domaines: Mathématiques [math]

Konstantinos Constantine Kyritsis. Alternative algebraic definitions of the Hessenberg natural operations in the ordinal numbers. [Research Report] National Technical University of Athens. 1995, http://users.softlab.ntua.gr/~kyritsis/PapersInMaths/InfinityandStochastics/AlterHA.htm. ⟨hal-01514107⟩