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arXiv · 1609.07694

Infinitely many reducts of homogeneous structures

Bertalan Bodor·Peter J. Cameron·Csaba Szabó
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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. Our construction over the 2-element field is related to the Reed--Muller codes.

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Bertalan Bodor, Peter J. Cameron, Csaba Szabó. 2016-09-25. Infinitely many reducts of homogeneous structures. https://doi.org/10.1007/s00012-018-0526-8

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