### Archives

### 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
- Genearlizations 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

Hedetniemi's conjecture Prikry-type forcing Selective Ultrafilter Successor of Regular Cardinal Non-saturation Knaster Chromatic number Reduced Power Souslin Tree Singular coﬁnality 05D10 Foundations Generalized Clubs Ascent Path Small forcing Poset middle diamond diamond star Universal Sequences weak square Fast club Almost countably chromatic PFA(S)[S] Minimal Walks Club Guessing Stevo Todorcevic OCA Cardinal Invariants Successor of Singular Cardinal 20M14 Martin's Axiom Fodor-type reflection Partition Relations Parameterized proxy principle Rock n' Roll Shelah's Strong Hypothesis stationary reflection Erdos Cardinal Rainbow sets Hindman's Theorem Ostaszewski square Forcing Slim tree incompactness reflection principles Cardinal function coloring number projective Boolean algebra Coherent tree very good scale Diamond stationary hitting Antichain polarized partition relation b-scale square Dushnik-Miller Almost Souslin approachability ideal Erdos-Hajnal graphs 11P99 Kurepa Hypothesis Weakly compact cardinal Axiom R Singular Cofinality ccc Uniformization Cohen real Commutative cancellative semigroups Absoluteness free Boolean algebra S-Space Singular Density Mandelbrot set Jonsson cardinal Fat stationary set L-space tensor product graph Forcing Axioms sap Hereditarily Lindelöf space 05A17 Whitehead Problem Aronszajn tree Chang's conjecture xbox P-Ideal Dichotomy HOD Constructible Universe Sakurai's Bell inequality Microscopic Approach Rado's conjecture weak diamond Large Cardinals Almost-disjoint famiy Singular cardinals combinatorics PFA Prevalent singular cardinals Square-Brackets Partition Relations

# 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