Pseudoalgebraically closed fields over rational function fields
Authors:
Moshe Jarden and Saharon Shelah
Journal:
Proc. Amer. Math. Soc. 87 (1983), 223228
MSC:
Primary 12F20; Secondary 12F99
MathSciNet review:
681825
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: The following theorem is proved: Let be an uncountable set of algebraically independent elements over a field . Then is a Hilbertian field but the set of for which is PAC is nonmeasurable.
 [1]
James
Ax, The elementary theory of finite fields, Ann. of Math. (2)
88 (1968), 239–271. MR 0229613
(37 #5187)
 [2]
, A mathematical approach to some problems in number theory, 1969 Number Theory Institute, Proc. Sympos. Pure Math., vol. 20, Amer. Math. Soc., Providence, R.I., 1971, pp. 161190.
 [3]
Gerhard
Frey, Pseudo algebraically closed fields with nonArchimedean real
valuations, J. Algebra 26 (1973), 202–207. MR 0325584
(48 #3931)
 [4]
Michael
Fried, Dan
Haran, and Moshe
Jarden, Galois stratification over Frobenius fields, Adv. in
Math. 51 (1984), no. 1, 1–35. MR 728998
(86c:12007), http://dx.doi.org/10.1016/00018708(84)900021
 [5]
Eizi
Inaba, Über den Hilbertschen Irreduzibilitätssatz,
Jap. J. Math. 19 (1944), 1–25 (German). MR 0016749
(8,62a)
 [6]
Moshe
Jarden, Elementary statements over large
algebraic fields, Trans. Amer. Math. Soc.
164 (1972),
67–91. MR
0302651 (46 #1795), http://dx.doi.org/10.1090/S00029947197203026519
 [7]
Moshe
Jarden, The elementary theory of 𝜔free Ax fields,
Invent. Math. 38 (1976/77), no. 2, 187–206. MR 0435051
(55 #8013)
 [8]
Moshe
Jarden, An analogue of Čebotarev density theorem for fields
of finite corank, J. Math. Kyoto Univ. 20 (1980),
no. 1, 141–147. MR 564673
(81d:12010)
 [9]
Moshe
Jarden and Ursel
Kiehne, The elementary theory of algebraic fields of finite
corank, Invent. Math. 30 (1975), no. 3,
275–294. MR 0435050
(55 #8012)
 [1]
 J. Ax, The elementary theory of finite fields, Ann. of Math. 88 (1968), 239271. MR 0229613 (37:5187)
 [2]
 , A mathematical approach to some problems in number theory, 1969 Number Theory Institute, Proc. Sympos. Pure Math., vol. 20, Amer. Math. Soc., Providence, R.I., 1971, pp. 161190.
 [3]
 G. Frey, Pseudoalgebraically closed fields with nonarchimedean real valuations, J. Algebra 26 (1973), 202207. MR 0325584 (48:3931)
 [4]
 M. Fried, D. Haran and M. Jarden, Galois stratification over Frobenius fields, Advances in Math. (to appear). MR 728998 (86c:12007)
 [5]
 E. Inaba, Über den Hilbertschen Irreduzibilitässatz, Japan. J. Math. 19 (1944), 125. MR 0016749 (8:62a)
 [6]
 M. Jarden, Elementary statements over large algebraic fields, Trans. Amer. Math. Soc. 164 (1972), 6797. MR 0302651 (46:1795)
 [7]
 , The elementary theory of free akfields, Invent. Math. 38 (1976), 187206. MR 0435051 (55:8013)
 [8]
 , An analogue of Čebotarev density theorem for fields of finite corank, J. Math. Kyoto Univ. 20 (1980), 141147. MR 564673 (81d:12010)
 [9]
 M. Jarden and U. Kiehne, The elementary theory of algebraic fields of finite corank, Invent. Math. 30 (1975), 275294. MR 0435050 (55:8012)
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC:
12F20,
12F99
Retrieve articles in all journals
with MSC:
12F20,
12F99
Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198306818254
PII:
S 00029939(1983)06818254
Keywords:
PAC fields,
Hilbertian fields,
Haar measure
Article copyright:
© Copyright 1983
American Mathematical Society
