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Generic automorphisms of fields

โœ Scribed by Angus Macintyre

Book ID
104307397
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
977 KB
Volume
88
Category
Article
ISSN
0168-0072

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โœฆ Synopsis

It is shown that the theory of fields with an automorphism has a decidable model companion.

Quantifier-elimination

is established in a natural language. The theory is intimately connected (via fixed fields) to Ax's theory of pseudofinite fields, and analogues are obtained for most of Ax's classical results. Some indication is given of the connection to nonstandard Frobenius maps.

๐Ÿ“œ SIMILAR VOLUMES

Automorphisms of finite fields
Automorphisms of finite fields
โœ H.W. Lenstra Jr. ๐Ÿ“‚ Article ๐Ÿ“… 1990 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 427 KB
Automorphisms of Medial Fields
Automorphisms of Medial Fields
โœ John L. Hickman ๐Ÿ“‚ Article ๐Ÿ“… 1982 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 371 KB

We recall from [l] that medial fields can exist in certain models of ZERMELO-FR~ESKEL set theory, and that if F is a medial field, then .F can be represented as the direct limit of a strictly increasing m-sequence (9n)lL<w of finite subfields. If we let 11 be the (necessarily nonzero) characteristic