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- The S-space problem, and the cardinal invariant $\mathfrak b$ April 4, 2013
- An $S$-space from a Cohen real April 3, 2013
- Forcing with a Souslin tree makes $\mathfrak p=\omega_1$ April 1, 2013
- The S-space problem, and the cardinal invariant $\mathfrak p$ March 28, 2013
- Jones’ theorem on the cardinal invariant $\mathfrak p$ March 26, 2013
- Erdős 100 March 26, 2013
- Bell’s theorem on the cardinal invariant $\mathfrak p$ March 21, 2013
- The $\Delta$-system lemma: an elementary proof March 20, 2013
Keywords
very good scale Square-Brackets Partition Relations Prevalent singular cardinals Aronszajn tree Hereditarily Lindelöf space reflection principles Minimal Walks incompactness projective Boolean algebra Ostaszewski square Erdos Cardinal Small forcing Poset square Club Guessing Chromatic number Souslin Tree polarized partition relation Knaster stationary reflection weak square Cohen real Prikry-type forcing Sakurai's Bell inequality Partition Relations approachability ideal Kurepa Hypothesis Mandelbrot set P-Ideal Dichotomy Axiom R middle diamond Non-saturation Forcing Large Cardinals Successor of Regular Cardinal Almost countably chromatic PFA(S)[S] stationary hitting Successor of Singular Cardinal Erdos-Hajnal graphs Dushnik-Miller free Boolean algebra Singular Cofinality Whitehead Problem Generalized Clubs Diamond S-Space Singular Density b-scale Singular cardinals combinatorics Rainbow sets Foundations weak diamond Antichain Rock n' Roll Rado's conjecture sap diamond star Cardinal function Shelah's Strong Hypothesis Uniformization
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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