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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

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

# Category Archives: Singular Cardinals Combinatorics

## Ordinal definable subsets of singular cardinals

Joint work with James Cummings, Sy-David Friedman, Menachem Magidor, and Dima Sinapova. Abstract. A remarkable result by Shelah states that if $\kappa$ is a singular strong limit cardinal of uncountable cofinality then there is a subset $x$ of $\kappa$ such … Continue reading

Posted in Publications, Singular Cardinals Combinatorics
Tagged HOD, Singular cardinals combinatorics
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## Aspects of singular cofinality

Abstract. We study properties of closure operators of singular cofinality, and introduce several ZFC sufficient and equivalent conditions for the existence of antichain sequences in posets of singular cofinality. We also notice that the Proper Forcing Axiom implies the Milner-Sauer … Continue reading

## 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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