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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

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

# 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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