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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

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

# 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