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