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higher Baire space C-sequence Fast club Local Club Condensation. Jonsson cardinal strongly bounded groups Sigma-Prikry Cardinal Invariants stationary hitting Hindman's Theorem Mandelbrot set Kurepa Hypothesis stick Ramsey theory over partitions b-scale Uniformization approachability ideal Fodor-type reflection Reduced Power Diamond for trees Analytic sets Prevalent singular cardinals SNR Hedetniemi's conjecture Erdos Cardinal Vanishing levels Filter reflection Uniformly coherent Large Cardinals Was Ulam right? Forcing Almost Souslin Fat stationary set Almost countably chromatic indecomposable ultrafilter AIM forcing Ascent Path Sierpinski's onto mapping principle Successor of Regular Cardinal Chang's conjecture very good scale Forcing Axioms Ulam matrix ccc P-Ideal Dichotomy Axiom R Precaliber Selective Ultrafilter Commutative projection system Strongly compact cardinal Small forcing projective Boolean algebra Minimal Walks Aronszajn tree ZFC construction Antichain Dushnik-Miller Well-behaved magma Successor of Singular Cardinal Dowker space tensor product graph transformations Subnormal ideal diamond star Poset xbox Souslin Tree Subadditive full tree Foundations Prikry-type forcing Respecting tree Strongly Luzin set Knaster and friends weak diamond Non-saturation Martin's Axiom countably metacompact L-space Almost-disjoint family polarized partition relation coloring number free Souslin tree Cohen real Diamond Square-Brackets Partition Relations Reflecting stationary set Rainbow sets Countryman line Coherent tree HOD nonmeager set super-Souslin tree positive partition relation Cardinal function Luzin set Generalized Clubs 54G20 Distributive tree Slim tree Universal Sequences Ostaszewski square Subtle cardinal Rado's conjecture Uniformly homogeneous stationary reflection weak Kurepa tree Absoluteness Intersection model GMA Greatly Mahlo PFA(S)[S] incompactness Subtle tree property unbounded function Shelah's Strong Hypothesis sap Iterated forcing Commutative cancellative semigroups Singular cardinals combinatorics Chromatic number Whitehead Problem Erdos-Hajnal graphs regressive Souslin tree Microscopic Approach Closed coloring Nonspecial tree Open Access Singular Density square weak square reflection principles Weakly compact cardinal Ineffable cardinal Sakurai's Bell inequality free Boolean algebra Partition Relations Hereditarily Lindelöf space Strong coloring specializable Souslin tree square principles Parameterized proxy principle PFA OCA Amenable C-sequence Diamond-sharp S-Space club_AD Club Guessing Constructible Universe middle diamond Generalized descriptive set theory Rock n' Roll Singular cofinality O-space Knaster Postprocessing function Lipschitz reduction
Category Archives: Publications
Full Souslin trees at small cardinals
Joint work with Shira Yadai and Zhixing You. Abstract. A
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
Posted in Partition Relations, Preprints, Topology
Tagged 03E02, 54G20, 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
Posted in Groups, Publications
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, 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
A new small Dowker space
Joint work with Roy Shalev and Stevo Todorcevic. Abstract. It is proved that if there exists a Luzin set, or if either the stick principle or
Was Ulam right? II: Small width and general ideals
Joint work with Tanmay Inamdar. Abstract. We continue our study of Sierpinski-type colourings. In contrast to the prequel paper, we focus here on colourings for ideals stratified by their completeness degree. In particular, improving upon Ulam’s theorem and its extension … Continue reading
Posted in Partition Relations, Publications
Tagged 03E02, 03E35, 03E55, C-sequence, Open Access, Subnormal ideal, Ulam matrix, Was Ulam right?
1 Comment
Complicated colorings, revisited
Joint work with Jing Zhang. Abstract. In a paper from 1997, Shelah asked whether
Sigma-Prikry forcing III: Down to Aleph_omega
Joint work with Alejandro Poveda and Dima Sinapova. Abstract. We prove the consistency of the failure of the singular cardinals hypothesis at
