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arXiv · 2111.14784

$\Theta$-Hilbertianity and strong $\Theta$-Hilbertianity

Sela Fried·Dan Haran
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Abstract

$\Theta$-Hilbertianity and its strengthening, strong $\Theta$-Hilbertianity, are two generalizations of Hilbertianity inspired by Jarden's definition of $p$-Hilbertianity and strong $p$-Hilbertianity. Jarden has asked whether the two notions defined by him are actually the same. We address this question in its more general version of $\Theta$-Hilbertianity and show that for PRC, and, in particular, for PAC fields, $p$-Hilbertianity and strong $p$-Hilbertianity coincide.

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Sela Fried, Dan Haran. 2021-11-25. $\Theta$-Hilbertianity and strong $\Theta$-Hilbertianity. https://arxiv.org/abs/2111.14784

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