### Archives

### 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

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

# 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
Leave a comment

## 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
Leave a comment