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arXiv · 2404.05265

Function spaces for orbit-finite sets

Mikołaj Bojańczyk·Lê Thành Dũng Nguyên·Rafał Stefański
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Abstract

Orbit-finite sets are a generalisation of finite sets, and as such support many operations allowed for finite sets, such as pairing, quotienting, or taking subsets. However, they do not support function spaces, i.e. if X and Y are orbit-finite sets, then the space of finitely supported functions from X to Y is not orbit-finite. In this paper we propose two solutions to this problem: one is obtained by generalising the notion of orbit-finite set, and the other one is obtained by restricting it. In both cases, function spaces and the original closure properties are retained. Curiously, both solutions are "linear": the generalisation is based on linear algebra, while the restriction is based on linear logic.

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Mikołaj Bojańczyk, Lê Thành Dũng Nguyên, Rafał Stefański. 2024-04-08. Function spaces for orbit-finite sets. https://arxiv.org/abs/2404.05265

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