The class of 2-dimensional neat reducts is not elementary

被引：13
|
作者：
Ahmed, TS [1 ]
机构：
[1] Cairo Univ, Fac Sci, Dept Math, Giza, Egypt
来源：
FUNDAMENTA MATHEMATICAE | 2002年 / 172卷 / 01期
关键词：
Algebraic Logic; cylindric algebras; quasipolyadic algebras; neat reducts; elementary;
D O I：
10.4064/fm172-1-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 Andreka and Nemeti on cylindric algebras, we show that for K E {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.
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页码：61 / 81
页数：21
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