Pseudo-finite field: Difference between revisions
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==References== |
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*{{Citation | last1=Ax | first1=James | title=The Elementary Theory of Finite Fields | |
*{{Citation | last1=Ax | first1=James | title=The Elementary Theory of Finite Fields | jstor=1970573 | publisher=Annals of Mathematics | series=Second Series | zbl=0195.05701 | mr=0229613 | year=1968 | journal=[[Annals of Mathematics]] | issn=0003-486X | volume=88 | issue=2 | pages=239–271 | doi=10.2307/1970573}} |
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* {{citation | last1=Fried | first1=Michael D. | last2=Jarden | first2=Moshe | title=Field arithmetic | edition=3rd revised | series=Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge | volume=11 | publisher=[[Springer-Verlag]] | year=2008 | isbn=978-3-540-77269-9 | zbl=1145.12001 | pages=448–453 }} |
* {{citation | last1=Fried | first1=Michael D. | last2=Jarden | first2=Moshe | title=Field arithmetic | edition=3rd revised | series=Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge | volume=11 | publisher=[[Springer-Verlag]] | year=2008 | isbn=978-3-540-77269-9 | zbl=1145.12001 | pages=448–453 }} |
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Revision as of 02:34, 14 November 2016
 | This article includes a list of general references, but it lacks sufficient corresponding inline citations. (December 2012) |
In mathematics, a pseudo-finite field F is an infinite model of the first-order theory of finite fields. This is equivalent to the condition that F is quasi-finite (perfect with a unique extension of every positive degree) and pseudo algebraically closed (every absolutely irreducible variety over F has a point defined over F). Every hyperfinite field is pseudo-finite and every pseudo-finite field is quasifinite. Every non-principal ultraproduct of finite fields is pseudo-finite.
Pseudo-finite fields were introduced by Ax (1968).
References
- Ax, James (1968), "The Elementary Theory of Finite Fields", Annals of Mathematics, Second Series, 88 (2), Annals of Mathematics: 239–271, doi:10.2307/1970573, ISSN 0003-486X, JSTOR 1970573, MR 0229613, Zbl 0195.05701
- Fried, Michael D.; Jarden, Moshe (2008), Field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 11 (3rd revised ed.), Springer-Verlag, pp. 448–453, ISBN 978-3-540-77269-9, Zbl 1145.12001