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