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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

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

# Tag Archives: Postprocessing function

## Distributive Aronszajn trees

Joint work with Ari Meir Brodsky. Abstract. Ben-David and Shelah proved that if $\lambda$ is a singular strong-limit cardinal and $2^\lambda=\lambda^+$, then $\square^*_\lambda$ entails the existence of a $\lambda$-distributive $\lambda^+$-Aronszajn tree. Here, it is proved that the same conclusion remains … Continue reading

## 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