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