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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

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

# 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