Second-Order Constructibility and HOD Without AC
An exposition on Szczepaniak's construction separating second-order constructibility from HOD in ZF
Two exercises that bugged me for a while
Two exercises about largest countable definable sets of reals under V=L
Two Alternative Proofs of Analytic Measurability
Proving analytic sets are measurable using recursion theory and forcing
Applications of a comeager null set
Size of ground model reals, generic reals, and Luzin (and Sierpinski) sets
Why is the Kleene-Brouwer order also called the Luzin-Sierpinski order?
Tracing its origin back in the Luzin-Sierpinski 1923 paper
Blackwell's Game-Theoretic Proof of Analytic Separation
Rewriting Blackwell's original argument in terms of trees
$\Pi^1_1$ set has a perfect subset if and only if it has nonconstructible element
An equivalent characterization of coanalytic thin sets in terms of constructibility
Silly proof of nonisomorphic uncountable linear orders using ordertypes of nonstandard models of arithmetic
All nonstandard models of arithmetic have ordertypes N+Zθ. None has ordertype N+ZR.
Being reals of a model of set theory a special property
Proof that reals in a model of set theory have inner measure zero if they are not all the reals
Three funny proofs of the existence of incomparable Turing degrees
Nuking incomparable mosquitoes with forcing, measure and category, and absoluteness
A perfect set of not-eventually-equal reals
clarification on a remark by Greg Hjorth
What's difficult about forcing?
An introductory overview of forcing, from the learner's perspective
Well-ordering of the reals is not measurable
An example of a nonmeasurable set that occurs in logic