### Archives

### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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