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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
- Genearlizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
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- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

### Keywords

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

# 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 Preprints, 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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