论文信息 - Addendum and Corrigendum: Choice Principles in Hyperuniverses

Addendum and Corrigendum: Choice Principles in Hyperuniverses

Abstract The proof of Lemma 5 in our paper “Choice Principles in Hyperuniverses” [3], contains an error. In the present note we show that the statement of that lemma is false and hence the Axiom of Choice fails in all κ-hyperuniverses, for uncountable κ. However, a weaker version of Lemma 5 can be proved, which implies that the Linear Ordering Principle holds in all κ-metric κ-hyperuniverses.

Furio Honsell | Marco Forti

[1] Furio Honsell,et al. Choice Principles in Hyperuniverses , 1996, Ann. Pure Appl. Log..

[2] Furio Honsell,et al. A General Construction of Hyperuniverses , 1996, Theor. Comput. Sci..

[3] Olivier Esser. An Interpretation of the Zermelo-Fraenkel Set Theory and the Kelley-Morse Set Theory in a Positive Theory , 1997, Math. Log. Q..