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Communication Dans Un Congrès Année : 2023

Ordinal measures of the set of finite multisets

Résumé

Well-partial orders, and the ordinal invariants used to measure them, are relevant in set theory, program verification, proof theory and many other areas of computer science and mathematics. In this article we focus on a common data structure in programming, finite multisets of some well partial order. There are two natural orders one can define on the set of finite multisets of a partial order: the multiset embedding and the multiset ordering. Though the maximal order type of these orders is already known, other ordinal invariants remain mostly unknown. Our main contributions are expressions to compute compositionally the width of the multiset embedding and the height of the multiset ordering. Furthermore, we provide a new ordinal invariant useful for characterizing the width of the multiset ordering.
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hal-04287405 , version 1 (15-11-2023)

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Isa Vialard. Ordinal measures of the set of finite multisets. MFCS 2023, Aug 2023, Bordeaux, France. ⟨10.4230/LIPIcs⟩. ⟨hal-04287405⟩
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