A difference field M , is a field with a distinguished endomorphism, is called
a generic difference field if it is existentially closed among the models of the
theory of difference fields. In the language Ld, by a theorem
of Hrushovski, it is characterized by the following: M is an algebraically closed
field, s is an automorphism of M, and if W and V are varieties defined over
M such that W is a subset of VU s (V ) and the projection maps W to V and
W to s(V ) are generically onto, then there is a tuple a in M such that
(a, s ( a)) in W. This thesis is a survey on the theory of generic difference
fields, called ACFA, which has been studied by Angus Macintyre, Van den
Dries, Carol Wood, Ehud Hrushovski and Zoe Chatzidakis. ACFA is the
model completion of the theory of algebraically closed difference fields. It
is very close to having full quantifier elimination, but it doesn' / t. We can
eliminate quantifiers down to formulas with one quantifier and hence obtain
the completions of ACFA. This entails the decidability of the theory ACFA
as well as its extensions obtained by specifying the characteristic. The fixed
field of s is a pseudo-finite field
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/766444/index.pdf |
| Date | 01 December 2003 |
| Creators | Yildirim, Irem |
| Contributors | Pierce, David |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | M.S. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for public access |
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