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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
- 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

### Keywords

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

# Tag Archives: Fodor-type reflection

## 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

## 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