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### Recent blog posts

- 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

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

# Tag Archives: Antichain

## 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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## 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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