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Disciplined Spaces and Centralizer Clone Segments

Published online by Cambridge University Press:  20 November 2018

V. Trnková  and
J. Sichler
V. Trnková
Affiliation:
Math. Institute of Charles University, Sokolovská 83, 186 00 Praha 8, Czech Republic e-mail: [email protected]
J. Sichler
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Canada, R3T 2N2 e-mail: [email protected]
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Abstract

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Our main result implies that for any choice 1 ≤ m ≤ n ≤ p of integers there exist finitary algebras A1 and A2 that generate the same variety, and such that the initial k-segments of their centralizer clones coincide exactly when k ≤ m, are isomorphic exactly when k ≤ n and are elementarily equivalent exactly when k ≤ p. The proof uses the existence and properties of disciplined topological spaces which we introduce and investigate here.

Keywords

08C0554C0508B2554E35clone segmentscontinuous maps of powers of metric spacescentralizer clones of universal algebras
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 6 , 01 December 1996 , pp. 1296 - 1323
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. Birkhoff, G. and Lipson, J. D., Heterogeneous algebras, J. Comb. Theory 8(1970), 115–133.Google Scholar
2. de Groot, J., Non∼archimedean metrics in topology, Proc. Amer. Math. Soc. 17(1956), 948–953.Google Scholar
3. Erdős, P. and Radó, R., A combinatorial theorem, J. London Math. Soc. 25(1950), 249–255.Google Scholar
4. Grätzer, G. A., Universal Algebra, 2nd Edition, Springer-Verlag, 1979.Google Scholar
5. McKenzie, R., A new product of algebras and a type reduction theorem, Algebra Universalis 8(1984), 26–69.Google Scholar
6. McKenzie, R., McNulty, G. and Taylor, W., Algebras, lattices, varieties, Volume 1, Brooks-Cole, Monterey, California, 1987.Google Scholar
7. Sichler, J. and Trnková, V., Isomorphism and elementary equivalence of clone segments, Period. Math. Hungar. 32(1996), 113–128.Google Scholar
8. Taylor, W., The clone of a topological space, Research and Exposition in Mathematics, vol. 13, Helderman Verlag, 1986.Google Scholar
9. Trnková, V., Semirigid spaces, Trans. Amer. Math. Soc. 343(1994), 305–325.Google Scholar
10. Trnkova, V., Algebraic theories, clones and centralizers, preprint, 1994.Google Scholar