Combinatorial Set Theory

DOI10.1007/978-1-4471-2173-2zbMath1237.03001OpenAlexW4247984777MaRDI QIDQ3094956

Lorenz Halbeisen

Publication date: 27 October 2011

Published in: Springer Monographs in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4471-2173-2

zbMATH Keywords

forcingcardinal invariantsiterated forcingRamsey theoremproper forcingcardinal numberordinal numberaxiomatic set theory

Mathematics Subject Classification ID

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations (03-01) Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations (03-02) Consistency and independence results (03E35) Continuum hypothesis and Martin's axiom (03E50) Axiomatics of classical set theory and its fragments (03E30) Other combinatorial set theory (03E05) Cardinal characteristics of the continuum (03E17) Ordinal and cardinal numbers (03E10) Axiom of choice and related propositions (03E25)

Related Items (22)

HIGHER INDEPENDENCE ⋮ Submaximal spaces and cardinal invariants ⋮ Coanalytic ultrafilter bases ⋮ Colourful categories ⋮ A weird relation between two cardinals ⋮ Preserving levels of projective determinacy by tree forcings ⋮ On countably compact group topologies without non-trivial convergent sequences on \(\mathbb{Q}^{(\kappa)}\) for arbitrarily large \(\kappa\) and a selective ultrafilter ⋮ Mathias and silver forcing parametrized by density ⋮ Some implications of Ramsey choice for families of \(n\)-element sets ⋮ Generalizations of Cantor's theorem in ⋮ Relations between cardinalities of the finite sequences and the finite subsets of a set ⋮ P-like properties of meager ideals and cardinal invariants ⋮ Remarks on generalized ultrafilter, dominating and reaping numbers ⋮ A model of \(\mathsf {ZFA}+ \mathsf {PAC}\) with no outer model of \(\mathsf {ZFAC}\) with the same pure part ⋮ On vector spaces over specific fields without choice ⋮ The spectrum of independence ⋮ Generalizing random real forcing for inaccessible cardinals ⋮ Toward an algebraic theory of systems ⋮ Ideals of independence ⋮ Banach spaces containing \(c_0\) and elements in the fourth dual ⋮ Convergence of measures in forcing extensions ⋮ Four cardinals and their relations in \textsf{ZF}

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