### 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

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

# 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