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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

### Keywords

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

# Tag Archives: Antichain

## Logic in Hungary 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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## 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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