### 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
- 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

### Keywords

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

# Tag Archives: Chang’s conjecture

## Reflection on the coloring and chromatic numbers

Joint work with Chris Lambie-Hanson. Abstract. We prove that reflection of the coloring number of a graph is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large … Continue reading

## 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