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Hindman's Theorem Ineffable cardinal Precaliber polarized partition relation transformations Sigma-Prikry Uniformization P-Ideal Dichotomy Interval topology on trees Hereditarily Lindelöf space stick Diamond for trees Respecting tree countably metacompact weak square Fodor-type reflection Uniformly coherent Sakurai's Bell inequality Hedetniemi's conjecture Forcing Axioms Cardinal function Forcing with side conditions Strong coloring Axiom R Diamond-sharp ZFC construction Chang's conjecture weak Kurepa tree sap Subtle cardinal Diamond Was Ulam right? Antichain square Ramsey theory over partitions Amenable C-sequence Non-saturation specializable Souslin tree reflection principles Closed coloring Aronszajn tree b-scale Singular cofinality stationary reflection Ostaszewski square full tree Small forcing Club Guessing Commutative cancellative semigroups GMA Erdos-Hajnal graphs Kurepa Hypothesis Prevalent singular cardinals Postprocessing function Universal Sequences very good scale Selective Ultrafilter Entangled linear order Rado's conjecture AIM forcing Minimal Walks Reflecting stationary set Poset Uniformly homogeneous Generalized Clubs Prikry-type forcing PFA(S)[S] Coherent tree free Boolean algebra nonmeager set Monotonically far approachability ideal Successor of Regular Cardinal Knaster and friends weak diamond Dowker space tensor product graph Knaster Jonsson cardinal Strongly Luzin set Luzin set Square-Brackets Partition Relations strongly bounded groups perfectly normal Ulam matrix positive partition relation Filter reflection middle diamond 54G20 Reduced Power Cardinal Invariants square principles Cohen real Open Access Dushnik-Miller OCA Rainbow sets Countryman line stationary hitting Sierpinski's onto mapping principle Chromatic number Weakly compact cardinal Almost-disjoint family Vanishing levels higher Baire space Successor of Singular Cardinal Singular Density Greatly Mahlo Constructible Universe Parameterized proxy principle Analytic sets Erdos Cardinal Fast club Commutative projection system Absoluteness unbounded function L-space Shelah's Strong Hypothesis Whitehead Problem Rock n' Roll club_AD Forcing Singular cardinals combinatorics Strongly compact cardinal PFA Lipschitz reduction Ascent Path Large Cardinals incompactness Well-behaved magma Distributive tree regressive Souslin tree SNR Nonspecial tree S-Space Ascending path O-space Generalized descriptive set theory Almost Souslin Foundations free Souslin tree Intersection model Subtle tree property Martin's Axiom diamond star xbox Local Club Condensation. Almost countably chromatic super-Souslin tree Subadditive Slim tree Partition Relations indecomposable filter Fat stationary set Subnormal ideal HOD ccc coloring number Microscopic Approach Mandelbrot set C-sequence Souslin Tree Iterated forcing projective Boolean algebra
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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