Nonembeddings of Combinatory Algebras

Patrick Lutz; Paul Shafer; Sebastiaan A. Terwijn

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arXiv · 2605.14701

Nonembeddings of Combinatory Algebras

Patrick Lutz·Paul Shafer·Sebastiaan A. Terwijn

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Abstract

In the theory of combinatorial algebras, there is a sequence of embeddings between Kleene's second model, van Oosten's model, and Scott's graph model. We prove that none of these embeddings can be reversed. We also prove nonembedding results for the effective versions of these models, and in addition we discuss relativized embeddings. This answers several questions from the literature.

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BibTeX RIS

Patrick Lutz, Paul Shafer, Sebastiaan A. Terwijn. 2026-05-14. Nonembeddings of Combinatory Algebras. https://arxiv.org/abs/2605.14701

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