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