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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
- 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

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

# 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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