Ordinal semigroups

Paolo Lipparini

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arXiv · 2605.28419

Ordinal semigroups

Paolo Lipparini

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Abstract

In a previous paper we introduced a version of associativity for a partial infinitary operation. We prove here that if $\gamma$ is an infinite ordinal and some associative infinitary operation is defined for all sequences indexed by ordinals $ \leq \gamma$, then such an operation can be uniquely expanded to apply to every sequence indexed by any ordinal of cardinality $ |\gamma |$. In particular, if some associative operation is defined for all finite sequences as well as for all $ \omega$-indexed sequences, then the operation can be uniquely expanded to apply to every sequence indexed by a countable ordinal.

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BibTeX RIS

Paolo Lipparini. 2026-05-27. Ordinal semigroups. https://arxiv.org/abs/2605.28419

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