$(\Theta\)-Hilbertianity and strong $\Theta$-Hilbertianity$

(\Theta\)-Hilbertianity and strong $\Theta$-Hilbertianity

$\Theta$-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 addr...

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Veröffentlicht in:	arXiv.org 2021-11
Hauptverfasser:	Fried, Sela, Haran, Dan
Format:	Artikel
Sprache:	eng
Online-Zugang:	Volltext
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Zusammenfassung:	$\Theta$-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.
ISSN:	2331-8422

Zusammenfassung:	\(\Theta\)-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.
ISSN:	2331-8422

(\Theta\)-Hilbertianity and strong \(\Theta\)-Hilbertianity