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