Talk:Implementation of mathematics in set theory: Difference between revisions

Revision as of 08:58, 23 December 2005

Revision as of 09:00, 23 December 2005

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: Unfortunately, that's the way I talk. But I will try to bear this in mind. [[User:Randall Holmes|Randall Holmes]] 08:54, 23 December 2005 (UTC)

: Re intended interpretation, see the model construction in the [[New Foundations]] article. The world of NFU is best understood to be an initial segment of the cumulative hierarchy with an external automorphism (which is then used to tweak the membership relation used). It actually presents some of the same difficulties you raised in your discussion of the intended interpretation of KM, with the additional feature that some elements of the NFU universe are clearly in some sense "nonstandard" (large ordinals moved by the T operation, for example). Another way of looking at NFU is to note that it is motivated more by the idea that a set is an abstraction from a predicate than by the idea of a set as a generalization (to the transfinite) of the everyday notion of set (a finite collection) [the latter being more what some say is going on in [[ZFC]]); but I don't see that this helps with getting a picture of what the world of NFU is like. [[User:Randall Holmes|Randall Holmes]] 08:54, 23 December 2005 (UTC)