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