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arXiv · 2511.17152

A Structural Account of Combinatory Completeness

Ivan Kuzmin·Chad Nester·Ülo Reimaa·Sam Speight
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Abstract

We give a general notion of combinatory completeness with respect to a faithful cartesian club and use it systematically to obtain characterisations of a number of different kinds of applicative system. Moreover, we characterise combinatory completeness of a given applicative system in terms of multicategory structure on its computable maps.

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Ivan Kuzmin, Chad Nester, Ülo Reimaa, Sam Speight. 2025-11-21. A Structural Account of Combinatory Completeness. https://arxiv.org/abs/2511.17152

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