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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Pseudo-algebraically closed fields over rational function fields


Authors: Moshe Jarden and Saharon Shelah
Journal: Proc. Amer. Math. Soc. 87 (1983), 223-228
MSC: Primary 12F20; Secondary 12F99
MathSciNet review: 681825
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Abstract: The following theorem is proved: Let $ T$ be an uncountable set of algebraically independent elements over a field $ {K_0}$. Then $ K = {K_0}(T)$ is a Hilbertian field but the set of $ \sigma \in G(K)$ for which $ \tilde K(\sigma )$ is PAC is nonmeasurable.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0681825-4
PII: S 0002-9939(1983)0681825-4
Keywords: PAC fields, Hilbertian fields, Haar measure
Article copyright: © Copyright 1983 American Mathematical Society