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Chang's conjecture Strongly Luzin set Chromatic number tensor product graph Successor of Regular Cardinal Constructible Universe Forcing Strongly compact cardinal Was Ulam right? Dowker space Generalized descriptive set theory Strong coloring Erdos-Hajnal graphs Lipschitz reduction Cardinal function Monotonically far Entangled linear order Distributive tree Diamond Forcing with side conditions Prevalent singular cardinals Forcing Axioms higher Baire space positive partition relation Uniformly coherent Iterated forcing sap ZFC construction Coherent tree Diamond-sharp HOD Poset Slim tree weak diamond Ascending path Nonspecial tree free Souslin tree square SNR OCA Axiom R Microscopic Approach Vanishing levels Countryman line Filter reflection Cardinal Invariants Subadditive Well-behaved magma reflection principles Selective Ultrafilter Local Club Condensation. coloring number Sigma-Prikry 54G20 Singular cardinals combinatorics incompactness Interval topology on trees Foundations Closed coloring Respecting tree Whitehead Problem Weakly compact cardinal Reduced Power Knaster Almost Souslin Baumgartner's square Shelah's Strong Hypothesis indecomposable filter Aronszajn tree Reflecting stationary set very good scale Ineffable cardinal Prikry-type forcing Fast club countably metacompact Hedetniemi's conjecture Erdos Cardinal weak Kurepa tree projective Boolean algebra Antichain Small forcing Intersection model full tree PFA super-Souslin tree Ostaszewski square ccc Partition relations for trees Sakurai's Bell inequality weak square diamond star Mandelbrot set Rado's conjecture GMA Club Guessing Greatly Mahlo Uniformization Postprocessing function Singular Density Universal Sequences square principles PFA(S)[S] Precaliber Large Cardinals Dushnik-Miller Singular cofinality free Boolean algebra Square-Brackets Partition Relations Parameterized proxy principle Successor of Singular Cardinal Fodor-type reflection Subtle tree property Kurepa Hypothesis Hindman's Theorem stationary hitting C-sequence perfectly normal S-Space unbounded function Hereditarily Lindelöf space nonmeager set Commutative projection system Subnormal ideal Partition Relations Luzin set Uniformly homogeneous Almost countably chromatic Absoluteness Martin's Axiom regressive Souslin tree O-space transformations Ramsey theory over partitions b-scale specializable Souslin tree club_AD polarized partition relation Commutative cancellative semigroups Amenable C-sequence Jonsson cardinal Almost-disjoint family Knaster and friends Open Access stationary reflection Ulam matrix approachability ideal Rock n' Roll Cohen real Subtle cardinal L-space Analytic sets strongly bounded groups Sierpinski's onto mapping principle Rainbow sets xbox AIM forcing Fat stationary set Diamond for trees Non-saturation middle diamond P-Ideal Dichotomy Souslin Tree stick Minimal Walks Generalized Clubs Ascent Path
Tag Archives: Open Access
Was Ulam right? III: Indecomposable ideals
Joint work with Tanmay Inamdar. Abstract. We continue our study of Ulam’s measure problem. In contrast to our previous works, we shift our focus from measures stratified by their additivity, to measures stratified by their indecomposability. The breakthrough here is … Continue reading
Diamond on Kurepa trees
Joint work with Ziemek Kostana and Saharon Shelah. Abstract. We introduce a new weak variation of diamond that is meant to guess only the branches of a Kurepa tree. We demonstrate that this variation is considerably weaker than diamond by … Continue reading
Proxy principles in combinatorial set theory
Joint work with Ari Meir Brodsky and Shira Yadai. Abstract. The parameterized proxy principles were introduced by Brodsky and Rinot in a 2017 paper as new foundations for the construction of $\kappa$-Souslin trees in a uniform way that does not … Continue reading
Squares, ultrafilters and forcing axioms
Joint work with Chris Lambie-Hanson and Jing Zhang. Abstract. We study the interplay of the three families of combinatorial objects or principles. Specifically, we show the following. Strong forcing axioms, in general incompatible with the existence of indexed squares, can … Continue reading
May the successor of a singular cardinal be Jonsson?
Abstract: Whether the successor of a singular cardinal can be Jónsson is a very old and famous open problem in set theory. Here, we collect necessary conditions for an affirmative answer, and put forward a list of closely-related questions in … Continue reading
Posted in Open Problems, Singular Cardinals Combinatorics
Tagged Jonsson cardinal, Open Access
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The vanishing levels of a tree
Joint work with Shira Yadai and Zhixing You. Abstract. We initiate the study of the spectrum of sets that can be realized as the vanishing levels $V(\mathbf T)$ of a normal $\kappa$-tree $\mathbf T$. This is an invariant in the … Continue reading
Posted in Preprints, Souslin Hypothesis
Tagged Almost-disjoint family, Ascent Path, C-sequence, Coherent tree, Dowker space, Open Access, Parameterized proxy principle, regressive Souslin tree, Respecting tree, Subtle tree property, Uniformly homogeneous, Vanishing levels, weak Kurepa tree
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Full Souslin trees at small cardinals
Joint work with Shira Yadai and Zhixing You. Abstract. A $\kappa$-tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $\kappa$-Souslin tree may consistently exist. Shelah gave an affirmative … Continue reading
A counterexample related to a theorem of Komjáth and Weiss
Joint work with Rodrigo Rey Carvalho. Abstract. In a paper from 1987, Komjath and Weiss proved that for every regular topological space $X$ of character less than $\mathfrak b$, if $X\rightarrow(\text{top }{\omega+1})^1_\omega$, then $X\rightarrow(\text{top }{\alpha})^1_\omega$ for all $\alpha<\omega_1$. In addition, … Continue reading
Posted in Partition Relations, Preprints, Topology
Tagged 03E02, 54G20, Open Access, Prikry-type forcing, ZFC construction
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A Shelah group in ZFC
Joint work with Márk Poór. Abstract. In a paper from 1980, Shelah constructed an uncountable group all of whose proper subgroups are countable. Assuming the continuum hypothesis, he constructed an uncountable group $G$ that moreover admits an integer $n$ satisfying … Continue reading
Posted in Groups, Publications
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, Open Access, Strong coloring, strongly bounded groups, Subadditive, ZFC construction
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