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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
- 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

### Keywords

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

# 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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