Monk Algebras and Representability
Year: 2025
Type: preprint
Abstract: In ``Monk Algebras and Ramsey Theory,'' \emph{J. Log. Algebr. Methods Program.} (2022), Kramer and Maddux prove various representability results in furtherance of the goal of finding the smallest weakly representable but not representable relation algebra. They also pose many open problems. In the present paper, we address problems and issues raised by Kramer and Maddux. In particular, we prove that their Proposition 7 does not generalize, and we answer Problem 1.1 in the negative: relation algebra $1311_{1316}$ is not representable. Thus $1311_{1316}$ is a good candidate for the smallest weakly representable but not representable relation algebra. Finally, we give the first known finite cyclic group representations for relation algebras $31_{37}$, $32_{65}$, $1306_{1314}$, and $1314_{1316}$.
Source: arXiv (Cornell University)
Author: Alm, Jeremy F.
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6929317352
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