### 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

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

# 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