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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

b-scale Antichain square principles Stevo Todorcevic Prevalent singular cardinals Small forcing Successor of Singular Cardinal stationary reflection Commutative cancellative semigroups PFA Rainbow sets Cardinal Invariants Uniformization sap Kurepa Hypothesis Microscopic Approach Axiom R square Singular coﬁnality Singular cardinals combinatorics Almost-disjoint famiy 05A17 Hedetniemi's conjecture Ostaszewski square Almost Souslin Minimal Walks Whitehead Problem reflection principles Poset Erdos Cardinal Martin's Axiom ccc stationary hitting Generalized Clubs tensor product graph Fast club P-Ideal Dichotomy Fat stationary set Cohen real Almost countably chromatic Postprocessing function approachability ideal very good scale Coherent tree Large Cardinals Nonspecial tree Uniformly coherent Slim tree Dushnik-Miller Mandelbrot set Partition Relations Aronszajn tree Hereditarily Lindelöf space Prikry-type forcing Weakly compact cardinal free Boolean algebra Parameterized proxy principle projective Boolean algebra weak square Shelah's Strong Hypothesis polarized partition relation Chromatic number Forcing Axioms S-Space Singular Density Non-saturation Universal Sequences weak diamond coloring number Foundations Souslin Tree middle diamond Diamond Club Guessing Chang's conjecture Distributive tree Knaster Fodor-type reflection 05D10 Selective Ultrafilter Forcing Hindman's Theorem Rado's conjecture Ascent Path Rock n' Roll L-space Square-Brackets Partition Relations diamond star Successor of Regular Cardinal Erdos-Hajnal graphs xbox Sakurai's Bell inequality incompactness 20M14 OCA Jonsson cardinal HOD Absoluteness 11P99 PFA(S)[S] Cardinal function Constructible Universe Reduced Power

# Tag Archives: Poset

## 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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