The class of 2-dimensional neat reducts is not elementary

Tarek Sayed Ahmed. "The class of 2-dimensional neat reducts is not elementary." Fundamenta Mathematicae 172.1 (2002): 61-81. <http://eudml.org/doc/283001>.

@article{TarekSayedAhmed2002,
abstract = {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.},
author = {Tarek Sayed Ahmed},
journal = {Fundamenta Mathematicae},
keywords = {algebraic logic; cylindric algebras; quasipolyadic algebras; neat reducts; substitution algebras; elementary subalgebras},
language = {eng},
number = {1},
pages = {61-81},
title = {The class of 2-dimensional neat reducts is not elementary},
url = {http://eudml.org/doc/283001},
volume = {172},
year = {2002},
}

TY - JOUR
AU - Tarek Sayed Ahmed
TI - The class of 2-dimensional neat reducts is not elementary
JO - Fundamenta Mathematicae
PY - 2002
VL - 172
IS - 1
SP - 61
EP - 81
AB - 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.
LA - eng
KW - algebraic logic; cylindric algebras; quasipolyadic algebras; neat reducts; substitution algebras; elementary subalgebras
UR - http://eudml.org/doc/283001
ER -