Surrealist landscape with figures (a survey of recent results in set theory)

DOI10.1007/BF02025889zbMath0417.03021OpenAlexW2051529371MaRDI QIDQ754865

Adrian R. D. Mathias

Publication date: 1979

Published in: Periodica Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02025889

zbMATH Keywords

scalessurveymetric spaceforcingMoore spacelarge cardinalsconstructibilitycontinuum hypothesisSouslin treeindependence resultsaxiom of choiceChang's conjecturedescriptive set theoryNew Foundationsfine structureindiscerniblesmodels of set theorystationary setsprojective hierarchyKurepa's conjectureaxiom of determinacyrelative consistencyaxiom systems of set theoryNeumann-Gödel-Bernays set theoryset theories with urelementsSilver machinessingular measurable and supercompact cardinals

Mathematics Subject Classification ID

Descriptive set theory (03E15) Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations (03-02) Consistency and independence results (03E35) Inner models, including constructibility, ordinal definability, and core models (03E45) Large cardinals (03E55) Continuum hypothesis and Martin's axiom (03E50) Nonclassical and second-order set theories (03E70) Other set-theoretic hypotheses and axioms (03E65) Axiom of choice and related propositions (03E25) Determinacy principles (03E60) Set theory (03Exx)

Related Items

Models of set theory in which the separation theorem fails, On the ‘definability of definable’ problem of Alfred Tarski, Part II, Dependences between definitions of finiteness, Forcing the Σ31-separation property, Set theory and the analyst, A good lightface \(\varDelta_n^1\) well-ordering of the reals does not imply the existence of boldface \(\mathbf{\Delta}_{n - 1}^1\) well-orderings, Singular Cardinals and the PCF Theory, A Property of Arithmetic Sets, A Souslin operation for \(\Pi^1_2\), Proofs of the Compactness Theorem, Mathias and set theory, On the consistency strength of accessible Jonsson cardinals and of the weak Chang conjecture, On the reducibility of \(\Pi_ 1^ 1\) sets, There are no P-points in Silver extensions, A Basis Theorem for Perfect Sets

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