Archives
Keywords
Closed coloring square full tree Singular cofinality b-scale sap Dowker space Coherent tree GMA Club Guessing Open Access Strong coloring Reflecting stationary set Local Club Condensation. Dushnik-Miller club_AD Shelah's Strong Hypothesis polarized partition relation Kurepa Hypothesis weak square Chang's conjecture AIM forcing weak diamond Minimal Walks Successor of Singular Cardinal Non-saturation Strongly Luzin set Prikry-type forcing Fat stationary set Erdos-Hajnal graphs Reduced Power xbox Well-behaved magma diamond star Analytic sets Diamond O-space Rainbow sets Chromatic number Was Ulam right Ramsey theory over partitions stationary hitting regressive Souslin tree transformations PFA OCA Souslin Tree Knaster Lipschitz reduction weak Kurepa tree nonmeager set Subtle tree property Sigma-Prikry Sierpinski's onto mapping principle Hereditarily Lindelöf space Ineffable cardinal Constructible Universe HOD Knaster and friends Microscopic Approach Subadditive Singular cardinals combinatorics Diamond for trees Foundations Iterated forcing Almost-disjoint family Fodor-type reflection ccc SNR Subtle cardinal Parameterized proxy principle Selective Ultrafilter Amenable C-sequence square principles Almost countably chromatic Large Cardinals free Boolean algebra Diamond-sharp positive partition relation Square-Brackets Partition Relations Uniformly homogeneous Generalized descriptive set theory Jonsson cardinal Greatly Mahlo specializable Souslin tree Subnormal ideal Uniformly coherent Vanishing levels Axiom R Martin's Axiom ZFC construction Absoluteness strongly bounded groups Slim tree very good scale Universal Sequences reflection principles Generalized Clubs incompactness Nonspecial tree Partition Relations P-Ideal Dichotomy Almost Souslin Rado's conjecture Postprocessing function Successor of Regular Cardinal Small forcing Sakurai's Bell inequality stationary reflection Hindman's Theorem unbounded function S-Space Aronszajn tree Rock n' Roll Mandelbrot set L-space Ulam matrix Poset super-Souslin tree stick Forcing Axioms Filter reflection tensor product graph Ascent Path Distributive tree Uniformization 54G20 Cardinal function free Souslin tree C-sequence Whitehead Problem Prevalent singular cardinals Hedetniemi's conjecture Ostaszewski square Commutative cancellative semigroups approachability ideal Erdos Cardinal Weakly compact cardinal Luzin set Precaliber countably metacompact coloring number Cohen real PFA(S)[S] indecomposable ultrafilter Fast club Forcing projective Boolean algebra higher Baire space middle diamond Singular Density Cardinal Invariants 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, weak Kurepa tree
Comments Off on Diamond on Kurepa trees
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
Comments Off on Proxy principles in combinatorial set theory
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
Comments Off on Squares, ultrafilters and forcing axioms
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
Comments Off on The vanishing levels of a tree
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
Comments Off on Full Souslin trees at small cardinals
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
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, Preprints
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, Strong coloring, strongly bounded groups, Subadditive, ZFC construction
2 Comments
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
Comments Off on A club guessing toolbox I