Abstract
We prove here the following theorems: A. If k is a denumerable Hilbertian field then for almost all ( σ 1 , … , σ e ) ∈ G ( k s / k ) e ({\sigma _1}, \ldots ,{\sigma _e}) \in \mathcal {G}{({k_s}/k)^e} the fixed field of { σ 1 , … , σ e } , k s ( σ 1 , … , σ e ) \{ {\sigma _1}, \ldots ,{\sigma _e}\} ,{k_s}({\sigma _1}, \ldots ,{\sigma _e}) , has the following property: For any non-void absolutely irreducible variety V defined over k s ( σ 1 , … , σ e ) {k_s}({\sigma _1}, \ldots ,{\sigma _e}) the set of points of V rational over K is not empty. B. If E is an elementary statement about fields then the measure of the set of σ ∈ G ( Q ~ / Q ) \sigma \in \mathcal {G}(\tilde Q/Q) (Q is the field of rational numbers) for which E holds in Q ~ ( σ ) \tilde Q(\sigma ) is equal to the Dirichlet density of the set of primes p for which E holds in the field F p {F_p} of p elements.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
