Sebastiaan A. Terwijn - Completions of Kleene's second model

lmcs:14230 - Logical Methods in Computer Science, June 4, 2025, Volume 21, Issue 2 - https://doi.org/10.46298/lmcs-21(2:17)2025
Completions of Kleene's second modelArticle

Authors: Sebastiaan A. Terwijn

    We investigate completions of partial combinatory algebras (pcas), in particular of Kleene's second model $\mathcal{K}_2$ and generalizations thereof. We consider weak and strong notions of embeddability and completion that have been studied before in the literature. It is known that every countable pca can be weakly embedded into $\mathcal{K}_2$, and we generalize this to arbitrary cardinalities by considering generalizations of $\mathcal{K}_2$ for larger cardinals. This emphasizes the central role of $\mathcal{K}_2$ in the study of pcas. We also show that $\mathcal{K}_2$ and its generalizations have strong completions.


    Volume: Volume 21, Issue 2
    Published on: June 4, 2025
    Accepted on: March 21, 2025
    Submitted on: September 10, 2024
    Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic

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