Geodesic
The class of 2-dimensional neat reducts is not elementary
Tarek Sayed Ahmed1
1 Department of Mathematics Faculty of Science Cairo University Giza, Egypt
Fundamenta Mathematicae, Tome 172 (2002) no. 1, pp. 61-81.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

$SC$, $CA$, $QA$ and $QEA$ stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras and Halmos' quasipolyadic algebras with equality, respectively. Generalizing a result of Andréka and Németi on cylindric algebras, we show that for $K\in \{SC,QA,CA,QEA\}$ and any $\beta >2$ the class of $2$-dimensional neat reducts of $\beta $-dimensional algebras in $K$ is not closed under forming elementary subalgebras, hence is not elementary. Whether this result extends to higher dimensions is open.
DOI : 10.4064/fm172-1-5
Keywords: qea stand classes pinters substitution algebras tarskis cylindric algebras halmos quasipolyadic algebras halmos quasipolyadic algebras equality respectively generalizing result andr meti cylindric algebras qea beta class dimensional neat reducts beta dimensional algebras closed under forming elementary subalgebras hence elementary whether result extends higher dimensions

Tarek Sayed Ahmed 1

1 Department of Mathematics Faculty of Science Cairo University Giza, Egypt 
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Tarek Sayed Ahmed. The class of 2-dimensional neat reducts is not elementary. Fundamenta Mathematicae, Tome 172 (2002) no. 1, pp. 61-81. doi : 10.4064/fm172-1-5. http://geodesic.mathdoc.fr/articles/10.4064/fm172-1-5/

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