Abstract
AbstractIn this paper three main results are presented: a bijection between natural sums and natural products, the completion of the axioms of Carruth for natural sums, and a new characterization of the natural sums in terms of Klaua’s integral ordinals. After introducing some preliminary results, we present two lemmas and a proposition for the proof of the existence of a bijection between natural products and natural sums. Then we prove the incompleteness of Carruth’s axioms by providing two counterexamples, and complete Carruth’s axioms by adding a fifth axiom. Finally, we introduce a characterization of natural sums in terms of Klaua’s integral ordinals and present two families of natural sums, which differ from Hessenberg’s sum.
Funder
Swiss Federal Institute of Technology Zurich
Publisher
Springer Science and Business Media LLC
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