Archives
Keywords
Successor of Regular Cardinal Hereditarily Lindelöf space Cohen real approachability ideal P-Ideal Dichotomy Axiom R stick Mandelbrot set Prikry-type forcing polarized partition relation Hedetniemi's conjecture Postprocessing function Reflecting stationary set Well-behaved magma ZFC construction weak Kurepa tree square principles Vanishing levels middle diamond Ulam matrix C-sequence AIM forcing stationary reflection super-Souslin tree Iterated forcing positive partition relation Martin's Axiom Aronszajn tree full tree Knaster and friends Ascent Path free Souslin tree Cardinal function Subtle cardinal countably metacompact Subnormal ideal Absoluteness stationary hitting PFA(S)[S] Poset reflection principles S-Space Forcing Axioms tensor product graph Fodor-type reflection Sigma-Prikry O-space Minimal Walks Uniformly coherent Strongly Luzin set xbox Dushnik-Miller higher Baire space OCA Sakurai's Bell inequality Subadditive diamond star HOD projective Boolean algebra Souslin Tree Cardinal Invariants Commutative cancellative semigroups Forcing b-scale Diamond-sharp Ostaszewski square Ramsey theory over partitions unbounded function specializable Souslin tree Erdos Cardinal Reduced Power Singular Density Coherent tree Successor of Singular Cardinal incompactness Selective Ultrafilter regressive Souslin tree Hindman's Theorem Chromatic number Antichain very good scale Weakly compact cardinal Foundations Generalized Clubs Filter reflection Open Access Almost countably chromatic indecomposable ultrafilter Club Guessing Almost Souslin Lipschitz reduction Non-saturation Diamond 54G20 Precaliber Partition Relations SNR Prevalent singular cardinals Strong coloring Distributive tree Rock n' Roll Dowker space Ineffable cardinal Kurepa Hypothesis Constructible Universe GMA Amenable C-sequence Closed coloring Chang's conjecture square PFA Uniformization Whitehead Problem Uniformly homogeneous Was Ulam right transformations Fat stationary set sap Small forcing Greatly Mahlo Sierpinski's onto mapping principle weak diamond Generalized descriptive set theory Parameterized proxy principle Square-Brackets Partition Relations Singular cardinals combinatorics strongly bounded groups Jonsson cardinal Local Club Condensation. coloring number Luzin set Microscopic Approach Large Cardinals Singular cofinality L-space Universal Sequences Almost-disjoint family Diamond for trees Shelah's Strong Hypothesis free Boolean algebra ccc club_AD Erdos-Hajnal graphs Rainbow sets Rado's conjecture Subtle tree property weak square Nonspecial tree Fast club nonmeager set Slim tree Analytic sets Knaster
Tag Archives: Sigma-Prikry
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 $\aleph_\omega$ together with the reflection of all stationary subsets of $\aleph_{\omega+1}$. This shows that two classical results of … Continue reading
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, and showed that many of the known Prikry-type notions of forcing that centers … Continue reading
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 $\Sigma$-Prikry, and show that many of the known Prikry-type notions of forcing that centers around singular cardinals of countable cofinality … Continue reading
