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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

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

# 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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