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### Recent blog posts

- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

### Keywords

Successor of Regular Cardinal polarized partition relation sap Chang's conjecture square principles Ostaszewski square L-space Fodor-type reflection weak square middle diamond coloring number very good scale Aronszajn tree Axiom R P-Ideal Dichotomy tensor product graph Foundations xbox square Martin's Axiom Almost countably chromatic Non-saturation weak diamond Uniformization Universal Sequences Singular Density Club Guessing Singular cardinals combinatorics Partition Relations stationary hitting Cardinal Invariants PFA Selective Ultrafilter projective Boolean algebra Singular coﬁnality Hereditarily Lindelöf space Generalized Clubs Rock n' Roll Absoluteness Uniformly coherent Microscopic Approach Kurepa Hypothesis diamond star Shelah's Strong Hypothesis Sakurai's Bell inequality Prevalent singular cardinals PFA(S)[S] Almost-disjoint famiy Hedetniemi's conjecture 20M14 Luzin set Stevo Todorcevic Ascent Path free Boolean algebra Large Cardinals Whitehead Problem Erdos-Hajnal graphs Commutative cancellative semigroups b-scale Hindman's Theorem Slim tree ccc S-Space super-Souslin tree Small forcing 05A17 Constructible Universe Diamond Souslin Tree 11P99 Fast club incompactness Poset Postprocessing function Successor of Singular Cardinal Erdos Cardinal Fat stationary set Rainbow sets Reduced Power Forcing Axioms Forcing stationary reflection Weakly compact cardinal Parameterized proxy principle Dushnik-Miller Rado's conjecture Coherent tree Cardinal function Square-Brackets Partition Relations approachability ideal HOD Jonsson cardinal Nonspecial tree Prikry-type forcing Distributive tree OCA Mandelbrot set Chromatic number Almost Souslin Minimal Walks Cohen real Antichain Knaster reflection principles

# Tag Archives: Absoluteness

## Mathematics Colloquium, Bar-Ilan University, November 2013

I gave a colloquium talk at Bar-Ilan University on November 10, 2013. Title: Forcing as a tool to prove theorems Abstract: Paul Cohen celebrated solution to Hilbert’s first problem showed that the Continuum Hypothesis is independent of the usual axioms of … Continue reading

## A large cardinal in the constructible universe

In this post, we shall provide a proof of Silver’s theorem that the Erdos caridnal $\kappa(\omega)$ relativizes to Godel’s constructible universe. First, recall some definitions. Given a function $f:[\kappa]^{<\omega}\rightarrow \mu$, we say that $I\subseteq\kappa$ is a set of indiscernibles for … Continue reading