### 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

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

# 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 graphs is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large gaps) … 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