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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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