### Archives

### 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

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

# Tag Archives: Postprocessing function

## A remark on Schimmerling’s question

Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether $\square^*_\lambda$ together with GCH entails the existence of a $\lambda^+$-Souslin tree, for a singular cardinal $\lambda$. Here, we provide an affirmative answer under the additional assumption that there exists a … Continue reading

## The 14th International Workshop on Set Theory in Luminy

I gave an invited talk at the 14th International Workshop on Set Theory in Luminy in Marseille, October 2017. Talk Title: Distributive Aronszajn trees Abstract: It is well-known that that the statement “all $\aleph_1$-Aronszajn trees are special” is consistent with ZFC … Continue reading

## 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