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Decidability and undecidability theorems for PAC-fields. (English) Zbl 0466.12017

MSC:
12L05 Decidability and field theory
03B25 Decidability of theories and sets of sentences
14G05 Rational points
20E18 Limits, profinite groups
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References:
[1] James Ax, The elementary theory of finite fields, Ann. of Math. (2) 88 (1968), 239 – 271. · Zbl 0195.05701
[2] Moshe Jarden, Rational points on algebraic varieties over large number fields, Bull. Amer. Math. Soc. 75 (1969), 603 – 606. · Zbl 0174.52702
[3] Moshe Jarden, The elementary theory of \?-free Ax fields, Invent. Math. 38 (1976/77), no. 2, 187 – 206. · Zbl 0342.12104
[4] M. Jarden and U. Kiehne, The elementary theory of algebraic fields of finite corank, Invent. Math. 30 (1975), 275-294. · Zbl 0315.12107
[5] A. Lubotzky and L. van den Dries, Subgroup of free profinite groups and large subfields of Q (submitted). · Zbl 0485.20021
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