Addendum and corrigendum Choice Principles in Hyperuniverses Annals of Pure and Applied Logic 77 (1996) 35–52

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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.

MSC

03E25
03E70
54C65
54E99

Keywords

Choice and ordering
Positive comprehension
Hyperuniverses

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