Infinitely many reducts of homogeneous structures
arXiv:1609.07694 · doi:10.1007/s00012-018-0526-8
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.