### 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

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

# 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