Pseudo algebraicallyc losed fields over rational function fields

Moshe Jarden; Saharon Shelah

doi:10.1090/S0002-9939-1983-0681825-4

Pseudo algebraicallyc losed fields over rational function fields

Moshe Jarden, Saharon Shelah

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

The following theorem is proved: Let T be an uncountable set of algebraically independent elements over a field K₀. Then K = K₀(T) is a Hilbertian field but the set of σ Є G(A") for which K(σ) is PAC is nonmeasurable.

Original language	English
Pages (from-to)	223-228
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	87
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1983-0681825-4
State	Published - Feb 1983

Keywords

Haar measure
Hilbertian fields
PAC fields

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10.1090/S0002-9939-1983-0681825-4

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title = "Pseudo algebraicallyc losed fields over rational function fields",

abstract = "The following theorem is proved: Let T be an uncountable set of algebraically independent elements over a field K0. Then K = K0(T) is a Hilbertian field but the set of σ Є G(A{"}) for which K(σ) is PAC is nonmeasurable.",

keywords = "Haar measure, Hilbertian fields, PAC fields",

author = "Moshe Jarden and Saharon Shelah",

year = "1983",

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doi = "10.1090/S0002-9939-1983-0681825-4",

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T1 - Pseudo algebraicallyc losed fields over rational function fields

AU - Jarden, Moshe

AU - Shelah, Saharon

PY - 1983/2

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N2 - The following theorem is proved: Let T be an uncountable set of algebraically independent elements over a field K0. Then K = K0(T) is a Hilbertian field but the set of σ Є G(A") for which K(σ) is PAC is nonmeasurable.

AB - The following theorem is proved: Let T be an uncountable set of algebraically independent elements over a field K0. Then K = K0(T) is a Hilbertian field but the set of σ Є G(A") for which K(σ) is PAC is nonmeasurable.

KW - Haar measure

KW - Hilbertian fields

KW - PAC fields

UR - https://www.scopus.com/pages/publications/84966219585

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AN - SCOPUS:84966219585

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SP - 223

EP - 228

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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ER -

Pseudo algebraicallyc losed fields over rational function fields

Abstract

Keywords

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