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### Recent blog posts

- 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

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

# 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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