Θ-Hilbertianity and strong Θ-Hilbertianity

Θ-Hilbertianity and strong Θ-Hilbertianity

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...

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Veröffentlicht in:Israel journal of mathematics 2023-11, Vol.257 (1), p.263-280
Hauptverfasser: Fried, Sela, Haran, Dan
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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Zusammenfassung: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.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-023-2528-2