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THE NEAT EMBEDDING PROBLEM FOR ALGEBRAS OTHER THAN CYLINDRIC ALGEBRAS AND FOR INFINITE DIMENSIONS

Published online by Cambridge University Press:  17 April 2014

ROBIN HIRSCH  and
TAREK SAYED AHMED
ROBIN HIRSCH
Affiliation:
DEPARTMENT OF COMPUTER SCIENCE, UNIVERSITY COLLEGE LONDON, GOWER STREET LONDON, WC1E 6BT, UKE-mail:ucacrdh@live.ucl.ac.uk
TAREK SAYED AHMED
Affiliation:
DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, CAIRO UNIVERSITY, GIZA, EGYPTE-mail: e-mail: rutahmed@gmail.com
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Abstract

Hirsch and Hodkinson proved, for $3 \le m < \omega $ and any $k < \omega $, that the class $SNr_m {\bf{CA}}_{m + k + 1} $ is strictly contained in $SNr_m {\bf{CA}}_{m + k} $ and if $k \ge 1$ then the former class cannot be defined by any finite set of first-order formulas, within the latter class. We generalize this result to the following algebras of m-ary relations for which the neat reduct operator $_m $ is meaningful: polyadic algebras with or without equality and substitution algebras. We also generalize this result to allow the case where m is an infinite ordinal, using quasipolyadic algebras in place of polyadic algebras (with or without equality).

Keywords

03G1503C10.Algebraic logic. cylindric algebras. quasi-polyadic algebras. substitution algebrasneat reductsneat embeddings
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 1 , March 2014 , pp. 208 - 222
Copyright
Copyright © Association for Symbolic Logic 2014 

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References

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