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diamond star Poset Rainbow sets sap Subnormal ideal L-space Subtle cardinal nonmeager set Erdos-Hajnal graphs Absoluteness Knaster and friends Prikry-type forcing Uniformly homogeneous tensor product graph Diamond Forcing middle diamond Closed coloring regressive Souslin tree Sierpinski's onto mapping principle Local Club Condensation. Singular Density OCA Cardinal Invariants Forcing Axioms Commutative cancellative semigroups Universal Sequences AIM forcing Small forcing Constructible Universe Ulam matrix Nonspecial tree Jonsson cardinal Erdos Cardinal countably metacompact Generalized descriptive set theory projective Boolean algebra Chang's conjecture Precaliber Cohen real Uniformly coherent Selective Ultrafilter Knaster Almost Souslin Ostaszewski square specializable Souslin tree Hindman's Theorem HOD Reduced Power Lipschitz reduction Well-behaved magma Rock n' Roll weak diamond Distributive tree Ascent Path free Souslin tree positive partition relation stationary hitting Luzin set incompactness Diamond-sharp P-Ideal Dichotomy Kurepa Hypothesis Aronszajn tree higher Baire space Square-Brackets Partition Relations Sakurai's Bell inequality Hereditarily Lindelöf space weak square Generalized Clubs Strongly Luzin set stationary reflection PFA S-Space Fast club b-scale Martin's Axiom Dushnik-Miller very good scale PFA(S)[S] Large Cardinals Partition Relations ccc approachability ideal Subadditive Rado's conjecture Minimal Walks Subtle tree property transformations reflection principles Open Access SNR square principles Dowker space Club Guessing unbounded function Coherent tree Almost-disjoint family Analytic sets Diamond for trees indecomposable ultrafilter Whitehead Problem Shelah's Strong Hypothesis square Parameterized proxy principle Postprocessing function Sigma-Prikry Foundations coloring number Filter reflection Non-saturation Was Ulam right Successor of Regular Cardinal club_AD Iterated forcing Ramsey theory over partitions Uniformization super-Souslin tree Singular cofinality Strong coloring Axiom R Mandelbrot set Greatly Mahlo Cardinal function C-sequence Singular cardinals combinatorics Slim tree full tree xbox Prevalent singular cardinals O-space Fat stationary set Microscopic Approach Hedetniemi's conjecture Almost countably chromatic Antichain free Boolean algebra Weakly compact cardinal 54G20 Souslin Tree GMA strongly bounded groups ZFC construction Vanishing levels Amenable C-sequence Fodor-type reflection Reflecting stationary set polarized partition relation Ineffable cardinal Chromatic number stick Successor of Singular Cardinal
Category Archives: Publications
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 only guess the branches of a Kurepa tree. We demonstrate that this variation is considerably weaker than diamond by … Continue reading
Posted in Preprints, Squares and Diamonds
Tagged Diamond, Diamond for trees, Iterated forcing, Kurepa Hypothesis
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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
Posted in Preprints, Souslin Hypothesis
Tagged C-sequence, free Souslin tree, Parameterized proxy principle, Souslin Tree, specializable Souslin tree, square principles, xbox
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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
Posted in Compactness, Preprints
Tagged Forcing Axioms, indecomposable ultrafilter, Subadditive, unbounded function
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May the successor of a singular cardinal be Jonsson?
Abstract: We collect necessary conditions for the successor of a singular cardinal to be Jónsson.
Posted in Open Problems, Singular Cardinals Combinatorics
Tagged Jonsson cardinal
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Perspectives on Set Theory, November 2023
I gave an invited talk at the Perspectives on Set Theory conference, November 2023. Talk Title: May the successor of a singular cardinal be Jónsson? Abstract: We’ll survey what’s known about the question in the title and collect ten open … Continue reading
Posted in Invited Talks, Open Problems, Partition Relations
Tagged Jonsson cardinal, Successor of Singular Cardinal
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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 $Vspec(\kappa)$ of sets that can be realized as the vanishing levels $V(\mathbf T)$ of a normal $\kappa$-tree $\mathbf T$. The latter is an invariant in … Continue reading
Posted in Preprints, Souslin Hypothesis
Tagged Almost-disjoint family, C-sequence, Coherent tree, Parameterized proxy principle, regressive Souslin tree, Subtle tree property, Uniformly homogeneous, Vanishing levels
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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
Posted in Preprints, Souslin Hypothesis
Tagged Diamond for trees, full tree, Greatly Mahlo, Microscopic Approach, Parameterized proxy principle, Subtle cardinal, tensor product graph
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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, 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, Preprints
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, Strong coloring, strongly bounded groups, Subadditive, ZFC construction
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