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- Genearlizations 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
- Walk on countable ordinals: the characteristics December 1, 2013
- Polychromatic colorings November 26, 2013
- Universal binary sequences November 14, 2013

### Keywords

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

# 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 Ordered Sets, Publications
Tagged 03E04, 03E05, 03E45, 03E55, 03E65, Large Cardinals, Poset, Shelah's Strong Hypothesis, Singular coﬁnality, Singular Density
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