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