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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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