Pseudofinite difference fields

Journal of Mathematical Logic 19 (2):1950011 (2019)
  Copy   BIBTEX

Abstract

We study a family of ultraproducts of finite fields with the Frobenius automorphism in this paper. Their theories have the strict order property and TP2. But the coarse pseudofinite dimension of the definable sets is definable and integer-valued. Moreover, we establish a partial connection between coarse dimension and transformal transcendence degree in these difference fields.

Categories

Keywords

Reprint years

DOI

10.1142/s0219061319500119

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,386

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

On algebraic closure in pseudofinite fields.Özlem Beyarslan & Ehud Hrushovski - 2012 - Journal of Symbolic Logic 77 (4):1057-1066.
Division rings whose vector spaces are pseudofinite.Vinicius Lopes & Lou van den Dries - 2010 - Journal of Symbolic Logic 75 (3):1087-1090.
Division rings whose vector spaces are pseudofinite.Lou Den Drievans & Vinicius Cifú Lopes - 2010 - Journal of Symbolic Logic 75 (3):1087-1090.
Division rings whose vector spaces are pseudofinite.Lou van den Dries & Vinicius Cifú Lopes - 2010 - Journal of Symbolic Logic 75 (3):1087 - 1090.
Pseudofinite Fields, Procyclic Fields and Model-Completion.Allan Adler & Catarina Kiefe - 1987 - Journal of Symbolic Logic 52 (4):1055-1055.
Review: Allan Adler, Catarina Kiefe, Pseudofinite Fields, Procyclic Fields and Model-Completion. [REVIEW]Alexander Prestel - 1987 - Journal of Symbolic Logic 52 (4):1055-1055.
Generic automorphisms of fields.Angus Macintyre - 1997 - Annals of Pure and Applied Logic 88 (2):165-180.
Coding Complete Theories in Galois Groups.James Gray - 2008 - Journal of Symbolic Logic 73 (2):474 - 491.
Disjoint $n$ -Amalgamation and Pseudofinite Countably Categorical Theories.Alex Kruckman - 2019 - Notre Dame Journal of Formal Logic 60 (1):139-160.
Model theory of finite and pseudofinite groups.Dugald Macpherson - 2018 - Archive for Mathematical Logic 57 (1-2):159-184.
Pseudofinite and Pseudocompact Metric Structures.Isaac Goldbring & Vinicius Cifú Lopes - 2015 - Notre Dame Journal of Formal Logic 56 (3):493-510.
Existentially closed ordered difference fields and rings.Françoise Point - 2010 - Mathematical Logic Quarterly 56 (3):239-256.
A note on existentially closed difference fields with algebraically closed fixed field.Anand Pillay - 2001 - Journal of Symbolic Logic 66 (2):719-721.
A Note On Existentially Closed Difference Fields With Algebraically Closed Fixed Field.Anand Pillay - 2001 - Journal of Symbolic Logic 66 (2):719-721.
Rank and Dimension in Difference-Differential Fields.Ronald F. Bustamante Medina - 2011 - Notre Dame Journal of Formal Logic 52 (4):403-414.

Analytics

Added to PP
2019-04-23

Downloads
19 (#778,470)

6 months
6 (#504,917)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Tingxiang Zou
Peking University

Citations of this work

No citations found.

Add more citations

References found in this work

Generic structures and simple theories.Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):71-92.
Laforte, G., see Downey, R.T. Arai, Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):287.
Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.
Pseudofinite structures and simplicity.Darío García, Dugald Macpherson & Charles Steinhorn - 2015 - Journal of Mathematical Logic 15 (1):1550002.
On Pseudo-Finite Dimensions.Ehud Hrushovski - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):463-495.

View all 7 references / Add more references