### 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

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

# Tag Archives: Erdos Cardinal

## Strong failures of higher analogs of Hindman’s Theorem

Joint work with David J. Fernández Bretón. Abstract. We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring $c:\mathbb R\rightarrow\mathbb Q$, such that … 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