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A Survey on the Model Theory of Difference Fields
, 2000
"... We survey the model theory of difference fields, that is, fields with a distinguished automorphism σ. After introducing the theory ACFA and stating elementary results, we discuss independence and the various concepts of rank, the dichotomy theorems, and, as an application, the Manin–Mumford conject ..."
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Cited by 67 (9 self)
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We survey the model theory of difference fields, that is, fields with a distinguished automorphism σ. After introducing the theory ACFA and stating elementary results, we discuss independence and the various concepts of rank, the dichotomy theorems, and, as an application, the Manin–Mumford conjecture over a number field. We conclude with some other applications.
Prospects for mathematical logic in the twentyfirst century
 BULLETIN OF SYMBOLIC LOGIC
, 2002
"... The four authors present their speculations about the future developments of mathematical logic in the twentyfirst century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently. ..."
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Cited by 8 (0 self)
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The four authors present their speculations about the future developments of mathematical logic in the twentyfirst century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently.
SUPERSIMPLE FIELDS AND DIVISION RINGS
 MATHEMATICAL RESEARCH LETTERS
, 1998
"... It is proved that any supersimple field has trivial Brauer group, and more generally that any supersimple division ring is commutative. As prerequisites we prove several results about generic types in groups and fields whose theory is simple. ..."
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Cited by 8 (2 self)
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It is proved that any supersimple field has trivial Brauer group, and more generally that any supersimple division ring is commutative. As prerequisites we prove several results about generic types in groups and fields whose theory is simple.
Elliptic and Hyperelliptic Curves Over Supersimple Fields
"... We prove that if F is an infinite field with characteristic di#erent from 2, whose theory is supersimple, and C is an elliptic or hyperelliptic curve over F with generic moduli then C has a generic F rational point. The notion of generity here is in the sense of the supersimple field F . ..."
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Cited by 3 (1 self)
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We prove that if F is an infinite field with characteristic di#erent from 2, whose theory is supersimple, and C is an elliptic or hyperelliptic curve over F with generic moduli then C has a generic F rational point. The notion of generity here is in the sense of the supersimple field F .