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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
- Genearlizations 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

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Almost-disjoint famiy Rock n' Roll Successor of Regular Cardinal Successor of Singular Cardinal Slim tree Coherent tree Fast club Sakurai's Bell inequality weak square Jonsson cardinal Mandelbrot set 05A17 Knaster Partition Relations stationary hitting Forcing Axioms Almost countably chromatic tensor product graph Dushnik-Miller Rado's conjecture Small forcing Erdos Cardinal Large Cardinals Club Guessing Universal Sequences square Non-saturation coloring number 20M14 05D10 sap Absoluteness Aronszajn tree Hereditarily Lindelöf space Fat stationary set OCA Axiom R Antichain stationary reflection Stevo Todorcevic Singular coﬁnality Constructible Universe Commutative cancellative semigroups Minimal Walks Generalized Clubs Rainbow sets Chang's conjecture Parameterized proxy principle Whitehead Problem Weakly compact cardinal Poset Reduced Power reflection principles diamond star Selective Ultrafilter approachability ideal 11P99 b-scale Forcing ccc Almost Souslin Erdos-Hajnal graphs Singular Cofinality P-Ideal Dichotomy Cohen real Martin's Axiom very good scale Fodor-type reflection Microscopic Approach free Boolean algebra Diamond xbox polarized partition relation HOD L-space projective Boolean algebra Shelah's Strong Hypothesis incompactness Souslin Tree S-Space middle diamond Square-Brackets Partition Relations Uniformization Ostaszewski square weak diamond Cardinal Invariants Kurepa Hypothesis Cardinal function Foundations Singular Density Singular cardinals combinatorics Prikry-type forcing Prevalent singular cardinals PFA(S)[S] Chromatic number Hindman's Theorem PFA Hedetniemi's conjecture Ascent Path

# 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