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

# 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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