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- 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

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