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