THE NEAT EMBEDDING PROBLEM FOR ALGEBRAS OTHER THAN CYLINDRIC ALGEBRAS
AND FOR INFINITE DIMENSIONS
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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).
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1995 ◽
Vol 15
(1)
◽
pp. 77-97
◽
1990 ◽
Vol 32
(2)
◽
pp. 180-192
◽