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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

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

# Tag Archives: stationary reflection

## MFO workshop in Set Theory, February 2017

I gave an invited talk at the Set Theory workshop in Obwerwolfach, February 2017. Talk Title: Coloring vs. Chromatic. Abstract: In a joint work with Chris Lambie-Hanson, we study the interaction between compactness for the chromatic number (of graphs) and … Continue reading

Posted in Invited Talks
Tagged Chromatic number, coloring number, incompactness, stationary reflection
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## The eightfold way

Joint work with James Cummings, Sy-David Friedman, Menachem Magidor, and Dima Sinapova. Abstract. Three central combinatorial properties in set theory are the tree property, the approachability property and stationary reflection. We prove the mutual independence of these properties by showing … 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

## The reflection principle $R_2$

A few years ago, in this paper, I introduced the following reflection principle: Definition. $R_2(\theta,\kappa)$ asserts that for every function $f:E^\theta_{<\kappa}\rightarrow\kappa$, there exists some $j<\kappa$ for which the following set is nonstationary: $$A_j:=\{\delta\in E^\theta_\kappa\mid f^{-1}[j]\cap\delta\text{ is nonstationary}\}.$$ I wrote there … Continue reading

Posted in Blog
Tagged reflection principles, square, stationary reflection, Weakly compact cardinal
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## Young Researchers in Set Theory, March 2011

These are the slides of a talk I gave at the Young Researchers in Set Theory 2011 meeting (Königswinter, 21–25 March 2011). Talk Title: Around Jensen’s square principle Abstract: Jensen‘s square principle for a cardinal $\lambda$ asserts the existence of a particular ladder … Continue reading

## Openly generated Boolean algebras and the Fodor-type reflection principle

Joint work with Sakaé Fuchino. Abstract: We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is $\aleph _2$-projective. Previously it was known that this … Continue reading

## The failure of diamond on a reflecting stationary set

Joint work with Moti Gitik. Abstract: It is shown that the failure of $\diamondsuit_S$, for a subset $S\subseteq\aleph_{\omega+1}$ that reflects stationarily often, is consistent with GCH and $\text{AP}_{\aleph_\omega}$, relatively to the existence of a supercompact cardinal. This should be comapred with … Continue reading

## A relative of the approachability ideal, diamond and non-saturation

Abstract: Let $\lambda$ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that $\square^*_\lambda$ together with $2^\lambda=\lambda^+$ implies $\diamondsuit_S$ for every $S\subseteq\lambda^+$ that reflects stationarily often. In this paper, for a subset $S\subset\lambda^+$, a normal subideal of … Continue reading