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seen Oct 24 at 12:23

Jul
8
comment Sets Constructible Relative To A Unary Predicate
This is theorem 13.22 (iii) in Jech's Set Theory book.
Jun
20
comment Covering $\mathbb R^2$ with function graphs
Another quote for the Sierpinski construction is in "Application of point set theory in real analysis" by A. B Kharazishvili p.188: assuming CH there is a single function that can be rotated or translated $\omega$ times and thus cover the plane.
Jun
16
comment Equivalent (?) definitions of Axiom A
The explanation makes sense, but I felt that some details are missing in J4=>B3.
Jun
16
comment Equivalent (?) definitions of Axiom A
Why are ordinal names the same as maximal antichains? I think that in order to show J4 => B3 we need to use the mixing lemma in order to build a name for a set $B$ that is too large.
Aug
23
comment Hausdorff theorem for any linear orders
In his papers from 1906 and 1907 "Investigations into Order Types" Hausdorff analyzes possible characteristics of special powers of ordered types (being dense, closed, homogeneous, continuous etc.). Do you know of any modern presentation of this survey?
Aug
9
comment Can't remember a number theory problem (from Hofstadter?)
In the book you qoute it appears in a dialog between the turtle and Achiles, after which Achiles betraid the turtle and hand him over to the cops.
Aug
2
comment Unprovability results in ZFC
The projection of $D$ or its complement on x-axis might be an uncountable comlpex non-Borel set. I don't see how the equation above (D=...) works.
Aug
2
comment Unprovability results in ZFC
nice. One question, why does "any subset of plane all of whose vertical sections are closed is in the sigma algebra generated by rectangles"?
Aug
1
comment Unprovability results in ZFC
Why are you looking at functions from R to R where we need subsets of the plan? Kanamori mentions the use of MA in Kunen's proof. For the other directions a lesser condition is needed, and Kunen used indescribability. Do you have access to the thesis?
Jul
31
comment Unprovability results in ZFC
Thanks for that, but the thesis itself is not available on the net. Do you have it by any chance? I would like to see the proof.
Jul
31
comment Unprovability results in ZFC
Can you please provide a reference to this thesis, or better yet a link?
Jun
12
comment Formalizing model-theoretical large cardinals in a formal system for ZFC
@Mario: Andres comments is correct, but I suggest you start with 1) a more accesible book like the one by Jech and Hrbacek, or Wikipedia 2) a lower level cardinal like measurable.
Jun
3
revised Exercise 24.13 of T. Jech's *Set Theory*
deleted 13 characters in body
Jun
3
revised Exercise 24.13 of T. Jech's *Set Theory*
added 26 characters in body
Jun
3
answered Exercise 24.13 of T. Jech's *Set Theory*
Jun
2
comment $\kappa <\operatorname{cf}(2^\kappa)$ without König's inequality
Then maybe this exercise was taken from Jech, as he explicitly says that the proof of theorem 3.11 does not rely on Konig's theorem.
Jun
1
answered $\kappa <\operatorname{cf}(2^\kappa)$ without König's inequality
May
12
comment Why does every countable limit ordinal have cofinality $\omega$?
By definition, a map from the least ordinal.
May
12
comment Why does every countable limit ordinal have cofinality $\omega$?
Cofinality is always a regular cardinal.
May
7
comment Powers of infinite cardinals in the generic extension
nope, but it doesn't really matter as we count all options (worst case is if it is 1-1).