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- Prikry forcing may add a Souslin tree June 12, 2016
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- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
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### Keywords

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

# 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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