= 27d567bc2d48d9f40e9ccc20ea370b15)
MrMind comments on Open Thread, September 30 - October 6, 2013 - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (295)
There's also the Axiom of Determinacy that rejects Choice and, when paired with the existence of a very strong measurable cardinal, gives a very broad class of measurable sets.
Could you give an example of a set whose measurability I might care about, other than subsets of R? something for random processes?
Could you give a reference for the combination?
Well, I guess this pretty much depends on the area you're working on. I'm interested in the foundation of mathematics, for which measurable sets are of big importance (for example, they are the smallest critical point of embedding of transitive models, or they are the smallest large cardinal property that cannot be shown to exists inside the smallest inner model). Outside of that area, I guess the interest is all about R and descriptive set theory.
Edit: It's not true that measurable cardinals are the smallest large cardinals that do not exists in L. Technically, the consistency strength is called 0#, and between that and measurables there are Ramsey cardinals.
Well, the definitive source is Kanamori's book "The higher infinite", but it's advanced. Some interesting things can be scooped up from Wikipedia's entry about the axiom of determinacy.