Answer by Gérard Lang for Order in bijective-equivalent collections of proper...
The answer to question 2 is Negative. This is because, answering to my question "Injection of the proper class of ordinals into every proper class", J.D. Hamkins proved on 02/12/2014 the existence in...
View ArticleAnswer by Joel David Hamkins for Order in bijective-equivalent collections of...
With regard to your first question, I claim that global choice is equivalent to the assertion that any two classes are comparable under injectivity. If global choice holds, then this is clearly the...
View ArticleAnswer by Asaf Karagila for Order in bijective-equivalent collections of...
In a previous question Joel Hamkins linked to a model obtained by adding Cohen subsets to every regular cardinal. This model had the property that the universe could not be linearly ordered.In...
View ArticleOrder in bijective-equivalent collections of proper classes in set-theory
We work in the set theory NBG (with local choice, but not global choice), because if there is global choice, every proper class is well-ordered, so that every proper class is bijective with the class...
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