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