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### 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

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

# 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