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 Feb7 revised Iterated ultrapowers with arbitrary measures are well-founded deleted 6 characters in body Feb7 answered Iterated ultrapowers with arbitrary measures are well-founded Jul8 comment Sets Constructible Relative To A Unary Predicate This is theorem 13.22 (iii) in Jech's Set Theory book. Jun20 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. Jun16 comment Equivalent (?) definitions of Axiom A The explanation makes sense, but I felt that some details are missing in J4=>B3. Jun16 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. Aug23 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? Aug9 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. Aug2 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. Aug2 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"? Aug1 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? Jul31 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. Jul31 comment Unprovability results in ZFC Can you please provide a reference to this thesis, or better yet a link? Jun12 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. Jun3 revised Exercise 24.13 of T. Jech's *Set Theory* deleted 13 characters in body Jun3 revised Exercise 24.13 of T. Jech's *Set Theory* added 26 characters in body Jun3 answered Exercise 24.13 of T. Jech's *Set Theory* Jun2 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. Jun1 answered $\kappa <\operatorname{cf}(2^\kappa)$ without König's inequality May12 comment Why does every countable limit ordinal have cofinality $\omega$? By definition, a map from the least ordinal.