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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

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

# 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