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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

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

# 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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