For finite n\geq 3, and k\geq 4, the variety SNr_n\CA_{n+k} is not atom canonical

Tarek Sayed Ahmed

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arXiv · 1306.1463

For finite n\geq 3, and k\geq 4, the variety SNr_n\CA_{n+k} is not atom canonical

Tarek Sayed Ahmed

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Abstract

We show that there exists an atomic representable polyadic equality algebra of finite dimension n\geq 3, such that the cylindric reduct of its completion is not in SNr_n\CA_{n+4}, hence the result in the title. This solves an open problem in algebraic logic, though the values for k=n+1, n+2, n+3, is still, to the best of our knowlege unknown.

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BibTeX RIS

Tarek Sayed Ahmed. 2013-06-04. For finite n\geq 3, and k\geq 4, the variety SNr_n\CA_{n+k} is not atom canonical. https://arxiv.org/abs/1306.1463

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