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

# 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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