Abstract
It is shown that the countably infinite dimensional pointed vector space (the vector space equipped with a constant) over a finite field has infinitely many first order definable reducts. This implies that the countable homogeneous Boolean-algebra has infinitely many reducts.
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This work is dedicated to Tamás E. Schmidt.
Presented by R. W. Quackenbush.
This article is part of the topical collection “In memory of E. Tamás Schmidt” edited by Robert W. Quackenbush.
The research of the first author was supported by the Hungarian OTKA K109185 grant and the second author was supported by the National Research, Development and Innovation Fund of Hungary, financed under the FK 124814 funding scheme.
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Bodor, B., Cameron, P.J. & Szabó, C. Infinitely many reducts of homogeneous structures. Algebra Univers. 79, 43 (2018). https://doi.org/10.1007/s00012-018-0526-8
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DOI: https://doi.org/10.1007/s00012-018-0526-8