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### Recent blog posts

- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014
- Walk on countable ordinals: the characteristics December 1, 2013
- Polychromatic colorings November 26, 2013
- Universal binary sequences November 14, 2013
- Syndetic colorings with applications to S and L October 26, 2013
- Open coloring and the cardinal invariant $\mathfrak b$ October 8, 2013
- Gabriel Belachsan (14/5/1976 – 20/8/2013) August 20, 2013

### Keywords

Diamond stationary hitting Erdos Cardinal weak diamond Forcing Axioms Souslin Tree Successor of Singular Cardinal Universal Sequences Kurepa Hypothesis Small forcing Successor of Regular Cardinal P-Ideal Dichotomy weak square Rado's conjecture Shelah's Strong Hypothesis Large Cardinals Hereditarily Lindelöf space Prevalent singular cardinals Foundations Partition Relations Cardinal Invariants b-scale very good scale Constructible Universe Singular cardinals combinatorics square diamond star Hedetniemi's conjecture middle diamond Axiom R Poset PFA(S)[S] OCA Minimal Walks Almost-disjoint famiy Chromatic number Antichain projective Boolean algebra sap Aronszajn tree Generalized Clubs approachability ideal Non-saturation Dushnik-Miller Square-Brackets Partition Relations tensor product graph Rock n' Roll Whitehead Problem Cohen real Singular Density Rainbow sets Prikry-type forcing Martin's Axiom incompactness free Boolean algebra Absoluteness reflection principles Almost countably chromatic Singular Cofinality Cardinal function polarized partition relation Forcing Knaster PFA Uniformization Erdos-Hajnal graphs stationary reflection L-space Mandelbrot set Ostaszewski square S-Space Sakurai's Bell inequality Club Guessing### Name Dropping

Ace Billet Alan Mekler Albin L. Jones Alex Primavesi Alfred Tarski András Hajnal Benoit Mandelbrot Boban Velickovic Chen Meiri Chris Hadfield Ernest Schimmerling Fred Glavin Gabriel Belachsan Hiroshi Sakai Ilijas Farah Itay Neeman Jack Silver Jim Baumgartner John Krueger Judy Roitman Keith Devlin Menachem Magidor Mirna Dzamonja Moti Gitik Murray Bell Paul Erdős Paul Larson Richard Laver Ronald Jensen Saharon Shelah Sakaé Fuchino Stevo Todorcevic Teruyuki Yorioka Wacław Sierpiński

# Tag Archives: 03E55

## 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

## On the consistency strength of the Milner-Sauer conjecture

Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The conjecture is consistent and known … Continue reading

Posted in Publications
Tagged 03E04, 03E05, 03E45, 03E55, 03E65, Large Cardinals, Poset, Shelah's Strong Hypothesis, Singular Cofinality, Singular Density
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