### 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

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

# 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