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 ∈ SC,QA,CA,QEA and any β > 2 the class of 2-dimensional neat reducts of β-dimensional algebras in K is not closed under forming elementary subalgebras, hence is not elementary. Whether this result extends to higher dimensions is open.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm172-1-5,
author = {Tarek Sayed Ahmed},
title = {The class of 2-dimensional neat reducts is not elementary},
journal = {Fundamenta Mathematicae},
volume = {173},
year = {2002},
pages = {61-81},
zbl = {0992.03083},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm172-1-5}
}
Tarek Sayed Ahmed. The class of 2-dimensional neat reducts is not elementary. Fundamenta Mathematicae, Tome 173 (2002) pp. 61-81. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm172-1-5/