### Archives

### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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