On atomicity of free algebras in certain cylindric-like varieties

Logic Journal of the IGPL 19 (1):44-52 (2011)
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Abstract

In this paper we show that the one-generated free three dimensional polyadic and substitutional algebras Fr1PA3 and Fr1SCA3 are not atomic. What is more, their corresponding logics have the Gödel’s incompleteness property. This provides a partial solution to a longstanding open problem of Németi and Maddux going back to Alfred Tarski via the book [12]

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10.1093/jigpal/jzp098

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Zalan Gyenis
Jagiellonian University

Citations of this work

First order logic without equality on relativized semantics.Amitayu Banerjee & Mohamed Khaled - 2018 - Annals of Pure and Applied Logic 169 (11):1227-1242.
The free non-commutative cylindric algebras are not atomic.Mohamed Khaled - 2017 - Logic Journal of the IGPL 25 (5):673-685.

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