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I am looking for the following PhD thesis, but could not find it, and all my attempts for finding it failed. I am wondering if there is a way to get it: On diagonalizations over complexity classes By: …

There are some statements, whose consistency (or the consistency of their negation) require the existence of large cardinals (in the sense that if the statement (or its negation) is consistent, then i …

There are different criteria for building a model $V$ of $ZFC$ which is far from its $HOD$, for example: $(A)$ Cardinality criteria: For this in a joint work with James Cummings and Sy Friedman, we …

Is there an elementary proof of van der Waerden's theorem on arithmetic progressions using probabilistic methods?

Recall that the Singular Cardinals Hypothesis (SCH) says that if $\kappa$ is a singular cardinal and $2^{cf(\kappa)}<\kappa,$ then $\kappa^{cf(\kappa)}=\kappa^+.$ Clearly it has many applications in s …

Is the following equiconsistent with the existence of a strongly compact cardinals: For every $\lambda > \kappa$ there exists a $\lambda$-strongly compact embedding $j: V \to M$ with the additiona …

In The sharp for the Chang model is small, Mitchell has stated a result of Woodin about the Chang's model, and he has produced a result using much weaker assumptions. As it is stated in the paper, t …

There are many unpublished results of Hugh Woodin on ''singular cardinals hypothesis'' and '' Radin forcing''. Some of his results are published later by others, but it seems that there are still many …

There are many $ZFC$ results that their proof uses forcing: The idea is that we force the statement to be true, and then using absoluteness (or other reasons) we conclude that the result is true in $Z …

This question is motivated by the answer of Gowers to the question Erdos Conjecture on arithmetic progressions. Question. (1)-Suppose $A \subset \mathbb{N}$ is such that Lim$_n$ $log(n) \cdot |A …

The question is essentially the one in the title. Question. What are some examples of (major) problems in set theory which are solved using techniques outside of mathematical logic?

It is well-known that if $V[G]$ is a generic extension by adding a Cohen real, then the set $\{r \in V[G]: r$ is Cohen generic over $V\}$ has measure zero. On the other hand, if $V[G]$ is a generic …

In set theory, starting from a model $V$ of $ZFC$, a forcing notion $\mathbb{P}$, and a generic filter $G \subset \mathbb{P}$ over $V$, we can find a generic extension which is a model of $ZFC$ and is …

I am looking for a comprehensive list of known forcing notions which add a minimal real into the ground model. I know some of them like the Sacks forcing, or the Judah-Shelah's example of a c.c.c. for …

Let me first recall some facts: By the work of Gowers, the Van der Waerden numbers belong to class $\mathcal{E}^3$ of the Grzegorczyk hierarchy By the work of Shelah, the Hales-Jewett numbers belon …