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

# Tag Archives: Singular coﬁnality

## Logic in Hungary, August 2005

These are the slides of a contributed talk given at the Logic in Hungary 2005 meeting (Budapest, 5–11 August 2005). Talk Title: On the consistency strength of the Milner-Sauer Conjecture Abstract: In their paper from 1981, after learning about Pouzet‘s theorem that any … Continue reading

Posted in Contributed Talks
Tagged Antichain, Shelah's Strong Hypothesis, Singular coﬁnality
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## 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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