On Pseudo-Finite Dimensions

Notre Dame Journal of Formal Logic 54 (3-4):463-495 (2013)
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Abstract

We attempt to formulate issues around modularity and Zilber’s trichotomy in a setting that intersects additive combinatorics. In particular, we update the open problems on quasi-finite structures from [9]

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10.1215/00294527-2143952

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Citations of this work

On $n$ -Dependence.Artem Chernikov, Daniel Palacin & Kota Takeuchi - 2019 - Notre Dame Journal of Formal Logic 60 (2):195-214.
Pseudofinite structures and simplicity.Darío García, Dugald Macpherson & Charles Steinhorn - 2015 - Journal of Mathematical Logic 15 (1):1550002.
Dividing and weak quasi-dimensions in arbitrary theories.Isaac Goldbring & Henry Towsner - 2015 - Archive for Mathematical Logic 54 (7-8):915-920.
Pseudofinite difference fields and counting dimensions.Tingxiang Zou - 2021 - Journal of Mathematical Logic 21 (1):2050022.

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References found in this work

Simple theories.Byunghan Kim & Anand Pillay - 1997 - Annals of Pure and Applied Logic 88 (2-3):149-164.
ℵ0-Categorical, ℵ0-stable structures.G. Cherlin, L. Harrington & A. H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
ℵ0-Categorical, ℵ0-stable structures.Gregory Cherlin, Leo Harrington & Alistair H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
Definability in reducts of algebraically closed fields.Gary A. Martin - 1988 - Journal of Symbolic Logic 53 (1):188-199.

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