Independence, Randomness and the Axiom of Choice

van Lambalgen, Michiel

J. Symbolic Logic, Tome 57 (1992) no. 1, p. 1274-1304 / Harvested from Project Euclid

Résumé

We investigate various ways of introducing axioms for randomness in set theory. The results show that these axioms, when added to ZF, imply the failure of AC. But the axiom of extensionality plays an essential role in the derivation, and a deeper analysis may ultimately show that randomness is incompatible with extensionality.

Publié le : 1992-12-14
Classification:

@article{1183744115,
     author = {van Lambalgen, Michiel},
     title = {Independence, Randomness and the Axiom of Choice},
     journal = {J. Symbolic Logic},
     volume = {57},
     number = {1},
     year = {1992},
     pages = { 1274-1304},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183744115}
}

van Lambalgen, Michiel. Independence, Randomness and the Axiom of Choice. J. Symbolic Logic, Tome 57 (1992) no. 1, pp.  1274-1304. http://gdmltest.u-ga.fr/item/1183744115/