We prove that the semialgebraic, algebraic, and algebraic nonsingular points of a definable set in o-minimal structure with analytic cell decomposition are definable. Moreover, the operation of taking semialgebraic points is idempotent and the degree of complexity of semialgebraic points is bounded.
@article{bwmeta1.element.bwnjournal-article-bcpv44i1p189bwm,
author = {Pi\k ekosz, Artur},
title = {On semialgebraic points of definable sets},
journal = {Banach Center Publications},
volume = {43},
year = {1998},
pages = {189-193},
zbl = {0920.03045},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv44i1p189bwm}
}
Piękosz, Artur. On semialgebraic points of definable sets. Banach Center Publications, Tome 43 (1998) pp. 189-193. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv44i1p189bwm/
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