### 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

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

# 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