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### 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

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