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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

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

# 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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