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- 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

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

# 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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