Talk:Measurable cardinal

message: I love your comment on the mistake in previus version. Another way is to use a model in which κ is not measurable but it becomes measurable after a forcing. Kunen has such a model. 157.181.80.93 11:15, 11 June 2006 (UTC)
replies: text: Yeah, I think 0# is right here. I also think the point made by the removed text, while interesting, is not one of the first 2,543 things you'd want to tell someone about measurable cardinals. Let's try to keep a little encyclopedic focus. --Trovatore 21:01, 6 August 2006 (UTC)
replies: text: Just happened to be looking here, and it occurred to me I should probably clarify -- I was saying Zero sharp was right that it's better for an article not to talk about itself, when it can be avoided. I don't actually know the result mentioned in point 2, and can't comment on the correctness of its statement (though I have no reason to doubt it). --Trovatore (talk) 03:56, 20 December 2007 (UTC)
replies: text: It's in the Dodd-Jensen covering lemma.Kope (talk) 07:50, 22 December 2007 (UTC)

text: Never the less its something I would find useful for my research.  Where can I find a statement of the ammended version of this result?  Barnaby dawson 16:58, 12 November 2007 (UTC)
thread_title: comments

message: The text says that the axiom of choice is used in the proof that a measurable cardinal κ is strongly inaccessible. However, I do not see where it is used. Can anyone show me? JRSpriggs (talk) 08:09, 12 February 2010 (UTC)
replies: text: I'd have to think about how it's used, but it's clearly needed.  For example AD implies that ω1 is a measurable cardinal.  So you need something that contradicts AD even to establish that a measurable cardinal must be weakly inaccessible. --Trovatore (talk) 06:42, 15 February 2010 (UTC)
replies: text: I must have been tired when I wrote that. The assumption AxCh is used implicitly in the form — either 2λ < κ or κ ≤ 2λ. JRSpriggs (talk) 08:27, 15 February 2010 (UTC)
thread_title:  Is AxCh needed for strong inaccessibility? 

message: So, I introduced a philosopher of science into the reference list. Why not? When it comes to large cardinals, mathematicians are little more than technically skilled philosophers themselves, and the referenced paper is good and mathematically "not wrong at all" as I understand it. Besides, I needed a reference for the layman description of a two-valued measure in the lead. I also added Jech, and hope to expand the article with some technical details in a (for a layman) readable way. 
Next to come, definition (mathematical) of two-valued measure and probably the Ulam matrix (will be detailed in that article) to support actual proof outlines of statements made here.
Then probably an illustration of the interconnection between two-valued measures and filters (and also ideals).
Violent protests are welcome! YohanN7 (talk) 17:45, 19 August 2015 (UTC)
replies: text: I don't see any problem with adding the link to Maddy's work.  (It doesn't reflect her current view, but that's OK; it's still a notable and influential one.)  I don't really know why you would expect "violent protests"; it seems quite a natural addition to me. --Trovatore (talk) 19:13, 19 August 2015 (UTC)
replies: text: "Violent protests are welcome!" should be read as "opinions on my plans are welcome". But I was tbh a little concerned about the Maddy reference, since it comes first of all, and might have been controversial.. YohanN7 (talk) 19:27, 19 August 2015 (UTC)
thread_title:  Philosophy 

message: The current Wikipedia article on cardinal number, https://en.wikipedia.org/wiki/Cardinal_number, defines cardinality in terms of an equivalence relation that is defined on a collection of sets.  By that definition, if the set S "has cardinality K", this indicates that S is a member of some ordered pair P of sets and that P is an member of the set K (since a "relation" like K consists of a set of ordered pairs).  So "subsets of S" are not the same collection of sets as "the subsets of K".  
However, the current article on "Measurable cardinal" seems to treat "the subsets of K" as if they were the same sets as "the subsets of a set S that has cardinality K".  This terminology may be a cultural tradition in discussing measurable sets.  If so, it should be mentioned. Tashiro~enwiki (talk) 17:43, 28 March 2017 (UTC)
replies: text: Please see my response to a related question here. JRSpriggs (talk) 20:24, 28 March 2017 (UTC)
thread_title:  "Subsets" of a cardinal number? 

message: I added a proof for two reasons:
* The proof is in itself notable in my opinion.
* The proof demonstrates that the mathematics of large cardinals need not always be totally inaccessible.
YohanN7 (talk) 11:11, 10 July 2017 (UTC)
thread_title:  Proof of inaccessibility of real-valued measurable cardinals