### 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
- 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

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

# 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