Measurable cardinals and the continuum hypothesis

From MaRDI portal
Publication:1846869

DOI10.1007/BF02771612zbMath0289.02044OpenAlexW2073171092MaRDI QIDQ1846869

Robert M. Solovay, Azriel Levy

Publication date: 1967

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02771612




Related Items (only showing first 100 items - show all)

Identity crises and strong compactness. III: Woodin cardinalsSome results on consecutive large cardinals. II: Applications of Radin forcingExactly controlling the non-supercompact strongly compact cardinalsAn AD-like modelIndestructibility properties of Ramsey and Ramsey-like cardinalsGap Forcing: Generalizing the Lévy-Solovay TheoremCoding into HOD via normal measures with some applicationsSome results concerning strongly compact cardinalsA Consistent Consequence of ADInstances of dependent choice and the measurability of \(\aleph _{\omega +1}\)Failures of SCH and level by level equivalenceChanging cofinalities and the nonstationary idealINDESTRUCTIBILITY WHEN THE FIRST TWO MEASURABLE CARDINALS ARE STRONGLY COMPACTThe least strongly compact can be the least strong and indestructibleOn certain indestructibility of strong cardinals and a question of HajnalPreserving levels of projective determinacy by tree forcingsThe first measurable cardinal can be the first uncountable regular cardinal at any successor heightPatterns of compact cardinalsSupercompactness and level by level equivalence are compatible with indestructibility for strong compactnessOn the consistency strength of level by level inequivalenceSaturated Ideals in Boolean ExtensionsIndestructibility properties of remarkable cardinalsGENERIC LARGE CARDINALS AS AXIOMSOn some questions concerning strong compactnessPrecisely controlling level by level behaviorInner models with large cardinal features usually obtained by forcingThe first omitting cardinal for MagidorityLarge cardinal structures below ℵωPrecipitous ideals and \(\sum^1_4\) setsOn weak square, approachability, the tree property, and failures of SCH in a choiceless contextSome structural results concerning supercompact cardinalsContinuity of coordinate functionals of filter bases in Banach spacesOn the least strongly compact cardinalIndestructibility of Vopěnka's principleA remark on the tree property in a choiceless contextIndestructible strong compactness but not supercompactnessMenas’ Result is Best PossibleCombinatorial properties and dependent choice in symmetric extensions based on Lévy collapseStrong combinatorial principles and level by level equivalenceLevel by level inequivalence beyond measurabilityThe Mathematical Development of Set Theory from Cantor to CohenAD and patterns of singular cardinals below ΘIdentity crises and strong compactnessOn tall cardinals and some related generalizationsBelieving the axioms. IIOn some properties of Shelah cardinalsHow many normal measures can ℵω1+1 carry?Borel canonization of analytic sets with Borel sectionsCertain very large cardinals are not created in small forcing extensionsOn a hypothesis for \({\aleph}_{0}\)-bounded groupsLarge Cardinals and the Continuum HypothesisGödel’s CantorianismThe scope of Feferman's semi-intuitionistic set theories and his second conjectureThe structure of the Mitchell order. II.Indestructibility and measurable cardinals with few and many measuresUniversal indestructibility for degrees of supercompactness and strongly compact cardinalsInner models from extended logics: Part 1Supercompactness and measurable limits of strong cardinalsAgainst the judgment-dependence of mathematics and logicCatch games: the impact of modeling decisionsLaver indestructibility and the class of compact cardinalsInaccessible cardinals, failures of GCH, and level-by-level equivalenceMeasurable cardinals and the cardinality of Lindelöf spacesOn some new metamathematical results concerning set theoryLevy and set theoryIndestructibility, instances of strong compactness, and level by level inequivalenceDiamond, square, and level by level equivalenceOn a problem of Foreman and MagidorIndestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal RestrictionsMartin's maximum\(^{++}\) implies Woodin's axiom \((*)\)The consistency strength of \(\aleph_\omega\) and \(\aleph_{\omega_1}\) being Rowbottom cardinals without the axiom of choiceMore on full reflection below \({\aleph_\omega}\)Normal measures and strongly compact cardinalsOn the singular cardinals problem. IOn measurable limits of compact cardinalsA note on tall cardinals and level by level equivalenceSet-theoretic geologyStrongly compact cardinals and the continuum functionOn the class of measurable cardinals without the axiom of choiceForcing the Least Measurable to Violate GCHAll uncountable cardinals in the Gitik model are almost Ramsey and carry Rowbottom filtersIndestructibility under adding Cohen subsets and level by level equivalence\(\omega_1\) can be measurableSuccessors of singular cardinals and measurability revisitedSurrealist landscape with figures (a survey of recent results in set theory)Successors of singular cardinals and measurabilityOn a problem of de Groot and a topological theorem of Ramsey typeTallness and level by level equivalence and inequivalenceIncompatible Ω-Complete TheoriesIndestructibility, measurability, and degrees of supercompactnessDEPENDENT CHOICE, PROPERNESS, AND GENERIC ABSOLUTENESSHow Woodin changed his mind: new thoughts on the continuum hypothesisLarge cardinals with few measuresSmall forcing creates neither strong nor Woodin cardinalsSome results on consecutive large cardinalsThe Significance of Relativistic Computation for the Philosophy of MathematicsLarge cardinals, inner models, and determinacy: an introductory overviewMeasurability and degrees of strong compactnessIndestructibility and the level-by-level agreement between strong compactness and supercompactnessOn index of total boundedness of (strictly) \(o\)-bounded groups



Cites Work


This page was built for publication: Measurable cardinals and the continuum hypothesis