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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

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

# 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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