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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

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

# Tag Archives: Antichain

## 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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## 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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