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- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- 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

### Keywords

Martin's Axiom Weakly compact cardinal Large Cardinals L-space Fat stationary set Reduced Power Ascent Path Small forcing Axiom R Chang's conjecture Aronszajn tree tensor product graph Parameterized proxy principle Stevo Todorcevic Partition Relations Almost Souslin Erdos Cardinal Ostaszewski square diamond star HOD coloring number incompactness reflection principles polarized partition relation Rock n' Roll stationary reflection stationary hitting Generalized Clubs Uniformization Slim tree Club Guessing Fodor-type reflection Whitehead Problem middle diamond approachability ideal Cohen real Rainbow sets Absoluteness Prevalent singular cardinals Chromatic number free Boolean algebra Constructible Universe PFA(S)[S] b-scale Singular Density OCA Antichain Universal Sequences projective Boolean algebra Hereditarily Lindelöf space Dushnik-Miller Poset weak square Coherent tree Shelah's Strong Hypothesis Forcing Axioms Forcing 05A17 Kurepa Hypothesis weak diamond 20M14 Microscopic Approach Commutative cancellative semigroups Cardinal function PFA Fast club Mandelbrot set Successor of Regular Cardinal Singular cardinals combinatorics Almost countably chromatic Almost-disjoint famiy Minimal Walks xbox Cardinal Invariants Souslin Tree Jonsson cardinal sap Prikry-type forcing Foundations P-Ideal Dichotomy Hedetniemi's conjecture very good scale square 05D10 Successor of Singular Cardinal Erdos-Hajnal graphs Rado's conjecture S-Space Square-Brackets Partition Relations Diamond Knaster Non-saturation Singular coﬁnality Hindman's Theorem Selective Ultrafilter ccc Singular Cofinality Sakurai's Bell inequality 11P99

# 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

## 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, Singular Cardinals Combinatorics
Tagged 03E04, 03E35, 06A07, Antichain, Poset, Singular coﬁnality
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