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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

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

# 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