### 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

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

# 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