### 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
- 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

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

# 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 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

## 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