Submission date: 25 November 2021

Abstract:

Θ-Hilbertianity and its strengthening, strong Θ-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 Θ-Hilbertianity and show that for PRC, and, in particular, for PAC fields, p-Hilbertianity and strong p-Hilbertianity coincide.

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Full text arXiv 2111.14784: pdf, ps.