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### 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

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

# 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