### 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

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

# 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