The first-order structure of weakly Dedekind-finite sets

Walczak-Typke, A. C.

J. Symbolic Logic, Tome 70 (2005) no. 1, p. 1161-1170 / Harvested from Project Euclid

Résumé

We show that infinite sets whose power-sets are Dedekind-finite can only carry ℵ₀-categorical first order structures. We identify other subclasses of this class of Dedekind-finite sets, and discuss their possible first order structures.

Publié le : 2005-12-14
Classification: axiom of choice, ℵ₀-categorical structures, Dedekind-finite

@article{1129642121,
     author = {Walczak-Typke, A. C.},
     title = {The first-order structure of weakly Dedekind-finite sets},
     journal = {J. Symbolic Logic},
     volume = {70},
     number = {1},
     year = {2005},
     pages = { 1161-1170},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1129642121}
}

Walczak-Typke, A. C. The first-order structure of weakly Dedekind-finite sets. J. Symbolic Logic, Tome 70 (2005) no. 1, pp.  1161-1170. http://gdmltest.u-ga.fr/item/1129642121/