### 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

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

# 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