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Recent blog posts
- 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
Small forcing polarized partition relation Kurepa Hypothesis square Dushnik-Miller Prikry-type forcing PFA(S)[S] Shelah's Strong Hypothesis Large Cardinals reflection principles Aronszajn tree sap Diamond Almost countably chromatic Knaster Singular Cofinality Souslin Tree Whitehead Problem very good scale P-Ideal Dichotomy Partition Relations Ostaszewski square free Boolean algebra Club Guessing Successor of Regular Cardinal weak square Forcing Foundations Prevalent singular cardinals Chromatic number Axiom R Erdos-Hajnal graphs Uniformization middle diamond Rainbow sets Successor of Singular Cardinal Generalized Clubs Rado's conjecture S-Space Erdos Cardinal incompactness Square-Brackets Partition Relations Singular cardinals combinatorics approachability ideal diamond star Antichain Singular Density stationary hitting Mandelbrot set weak diamond Minimal Walks Cardinal function Sakurai's Bell inequality stationary reflection Cohen real Hereditarily Lindelöf space projective Boolean algebra b-scale Non-saturation Poset Rock n' Roll
Tag Archives: Poset
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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Antichains in partially ordered sets of singular cofinality
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 main result of of this … Continue reading
Posted in Publications
Tagged 03E04, 03E35, 06A07, Antichain, Poset, Singular Cofinality
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