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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

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

# 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