### 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

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

# 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