Pseudo-finite field: Difference between revisions

Content deleted Content added

Inline

Revision as of 07:24, 12 November 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 a quasi-finite field such that for every finitely generated absolutely entire F-algebra R there is an F-homomorphism from R to F, and to the condition that F is a quasi-finite field such that 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, ISSN 0003-486X, 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

@@ Line 4: / Line 4: @@
 ==References==
+{{reflist}}
 *{{Citation | last1=Ax | first1=James | title=The Elementary Theory of Finite Fields | url=http://www.jstor.org/stable/1970573 | publisher=Annals of Mathematics | language=English | series=Second Series | zbl=0195.05701 | mr=0229613 | year=1968 | journal=[[Annals of Mathematics]] | issn=0003-486X | volume=88 | issue=2 | pages=239–271}}
+* {{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 }}
 [[Category:Model theory]]