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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
- 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

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

# 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