### Archives

### 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
- Genearlizations 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

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

# Tag Archives: stationary reflection

## 2017 Workshop in Set Theory, Oberwolfach

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 a graph is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large … 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 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