### 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

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

# 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