### 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

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

# 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