The First-Order Structure of Weakly Dedekind-Finite Sets

Journal of Symbolic Logic 70 (4):1161 - 1170 (2005)
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Abstract

We show that infinite sets whose power-sets are Dedekind-finite can only carry N₀-categorical first order structures. We identify other subclasses of this class of Dedekind-finite sets, and discuss their possible first order structures

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10.2178/jsl/1129642121

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Citations of this work

A dedekind finite borel set.Arnold W. Miller - 2011 - Archive for Mathematical Logic 50 (1-2):1-17.

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References found in this work

ℵ0-Categorical, ℵ0-stable structures.G. Cherlin, L. Harrington & A. H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
The structure of amorphous sets.J. K. Truss - 1995 - Annals of Pure and Applied Logic 73 (2):191-233.
Some Aspects and Examples of Infinity Notions.J. W. Degen - 1994 - Mathematical Logic Quarterly 40 (1):111-124.
On o-amorphous sets.P. Creed & J. K. Truss - 2000 - Annals of Pure and Applied Logic 101 (2-3):185-226.

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