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PFA(S)[S] Rainbow sets Knaster Kurepa Hypothesis Erdos-Hajnal graphs b-scale Sakurai's Bell inequality tensor product graph countably metacompact specializable Souslin tree Reduced Power Universal Sequences projective Boolean algebra Ulam matrix Erdos Cardinal weak diamond Shelah's Strong Hypothesis Mandelbrot set Dushnik-Miller O-space Weakly compact cardinal Subtle cardinal Sigma-Prikry Prikry-type forcing Fodor-type reflection OCA Sierpinski's onto mapping principle stationary hitting free Souslin tree Coherent tree Fat stationary set Almost Souslin coloring number Strongly Luzin set Well-behaved magma weak Kurepa tree Slim tree Square-Brackets Partition Relations Microscopic Approach xbox middle diamond Uniformly homogeneous indecomposable ultrafilter positive partition relation sap Iterated forcing diamond star free Boolean algebra Knaster and friends P-Ideal Dichotomy Uniformly coherent Whitehead Problem Axiom R Martin's Axiom ZFC construction Souslin Tree Postprocessing function Foundations Intersection model Strongly compact cardinal Ineffable cardinal Diamond weak square Open Access Jonsson cardinal AIM forcing nonmeager set transformations Closed coloring square principles Subtle tree property Hindman's Theorem Cardinal Invariants Non-saturation Generalized Clubs strongly bounded groups Forcing stationary reflection Generalized descriptive set theory S-Space incompactness HOD Countryman line ccc Subnormal ideal 54G20 reflection principles Commutative projection system Cardinal function Precaliber Small forcing Diamond for trees Rock n' Roll Chromatic number L-space Aronszajn tree C-sequence Constructible Universe Absoluteness Ascent Path Partition Relations Strong coloring Dowker space Analytic sets Singular cardinals combinatorics polarized partition relation Successor of Regular Cardinal Antichain Uniformization Forcing Axioms Commutative cancellative semigroups Was Ulam right? approachability ideal Local Club Condensation. Prevalent singular cardinals stick super-Souslin tree Large Cardinals full tree club_AD Poset Ostaszewski square very good scale Hereditarily Lindelöf space regressive Souslin tree Club Guessing Fast club unbounded function SNR Subadditive Minimal Walks Diamond-sharp Chang's conjecture Lipschitz reduction higher Baire space GMA Distributive tree Vanishing levels Luzin set Reflecting stationary set PFA Almost countably chromatic Rado's conjecture square Greatly Mahlo Hedetniemi's conjecture Respecting tree Selective Ultrafilter Amenable C-sequence Cohen real Ramsey theory over partitions Successor of Singular Cardinal Nonspecial tree Filter reflection Singular Density Singular cofinality Almost-disjoint family Parameterized proxy principle
Tag Archives: Successor of Singular Cardinal
Perspectives on Set Theory, November 2023
I gave an invited talk at the Perspectives on Set Theory conference, November 2023. Talk Title: May the successor of a singular cardinal be Jónsson? Abstract: We’ll survey what’s known about the question in the title and collect ten open … Continue reading
Posted in Invited Talks, Open Problems
Tagged Jonsson cardinal, Successor of Singular Cardinal
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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
Sigma-Prikry forcing II: Iteration Scheme
Joint work with Alejandro Poveda and Dima Sinapova. Abstract. In Part I of this series, we introduced a class of notions of forcing which we call
Sigma-Prikry forcing I: The Axioms
Joint work with Alejandro Poveda and Dima Sinapova. Abstract. We introduce a class of notions of forcing which we call
Putting a diamond inside the square
Abstract. By a 35-year-old theorem of Shelah,
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Diamond, square, Successor of Singular Cardinal
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A cofinality-preserving small forcing may introduce a special Aronszajn tree
Extended Abstract: Shelah proved that Cohen forcing introduces a Souslin tree; Jensen proved that a c.c.c. forcing may consistently add a Kurepa tree; Todorcevic proved that a Knaster poset may already force the Kurepa hypothesis; Irrgang introduced a c.c.c. notion … Continue reading
Posted in Publications, Squares and Diamonds
Tagged 03E04, 03E05, 03E35, Aronszajn tree, Small forcing, Successor of Singular Cardinal, weak square
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The failure of diamond on a reflecting stationary set
Joint work with Moti Gitik. Abstract: It is shown that the failure of
A relative of the approachability ideal, diamond and non-saturation
Abstract: Let
Transforming rectangles into squares, with applications to strong colorings
Abstract: It is proved that every singular cardinal
