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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

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

# Tag Archives: Singular coﬁnality

## 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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