Elimination theory for addition and the Frobenius map in polynomial rings

&
Journal of Symbolic Logic 69 (4):1006-1026 (2004)
  Copy   BIBTEX

Abstract

We develop an elimination theory for addition and the Frobenius map over rings of polynomials. As a consequence we show that if F is a countable, recursive and perfect field of positive characteristic p, with decidable theory, then the structure of addition, the Frobenius map x→ xp and the property ‘x∈ F', over the ring of polynomials F[T], has a decidable theory.

Categories

Keywords

Reprint years

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 106,716

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Model Theory of Derivations of the Frobenius Map Revisited.Jakub Gogolok - 2023 - Journal of Symbolic Logic 88 (3):1213-1229.
Derivations of the Frobenius map.Piotr Kowalski - 2005 - Journal of Symbolic Logic 70 (1):99-110.
Interpreting arithmetic in the first-order theory of addition and coprimality of polynomial rings.Javier Utreras - 2019 - Journal of Symbolic Logic 84 (3):1194-1214.
Rings which admit elimination of quantifiers.Bruce I. Rose - 1978 - Journal of Symbolic Logic 43 (1):92-112.
Valued fields with a total residue map.Konstantinos Kartas - 2023 - Journal of Mathematical Logic 24 (3).
Expansions of the p‐adic numbers that interpret the ring of integers.Nathanaël Mariaule - 2020 - Mathematical Logic Quarterly 66 (1):82-90.
Valued fields with a total residue map.Konstantinos Kartas - 2023 - Journal of Mathematical Logic 24 (3).
Elementary equivalence of some rings of definable functions.Vincent Astier - 2008 - Archive for Mathematical Logic 47 (4):327-340.
Elementary properties of power series fields over finite fields.Franz-Viktor Kuhlmann - 2001 - Journal of Symbolic Logic 66 (2):771-791.
Generic automorphisms of fields.Angus Macintyre - 1997 - Annals of Pure and Applied Logic 88 (2):165-180.

Analytics

Added to PP
2010-08-24

Downloads
39 (#648,676)

6 months
12 (#298,089)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Karim Zahidi
University of Antwerp

Citations of this work

No citations found.

Add more citations

References found in this work

Model theory of modules.Martin Ziegler - 1984 - Annals of Pure and Applied Logic 26 (2):149-213.
Book Reviews. [REVIEW]Wilfrid Hodges - 1997 - Studia Logica 64 (1):133-149.

Add more references