MAD families and strategically bounding forcings

DOI10.1007/s40879-021-00512-6OpenAlexW4210448472MaRDI QIDQ2115340

Osvaldo Guzmán González, Michael Hrušák

Publication date: 15 March 2022

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

Full work available at URL: https://doi.org/10.1007/s40879-021-00512-6

zbMATH Keywords

forcingcardinal invariantsMAD familiesbounding forcingsstrategically bounding

Mathematics Subject Classification ID

Consistency and independence results (03E35) Other combinatorial set theory (03E05) Cardinal characteristics of the continuum (03E17)

Cites Work

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• Bounding, splitting, and almost disjointness
• Template iterations with non-definable ccc forcing notions
• More game-theoretic properties of Boolean algebras
• Some weak fragments of Martin's axiom related to the rectangle refining property
• Forcing with quotients
• CON(\(\mathfrak u>\mathfrak i\))
• Partition numbers
• A model with no strongly separable almost disjoint families
• Forcing indestructibility of MAD families
• Two cardinal invariants of the continuum \(({\mathfrak d} <{\mathfrak a})\) and FS linearly ordered iterated forcing
• Free sequences in \({\mathscr{P}}( \omega) /\mathrm{fin}\)
• Matrix iterations and Cichon's diagram
• On Pospíšil ideals
• Another ♦-like principle
• Cohen-stable families of subsets of integers
• MATHIAS FORCING AND COMBINATORIAL COVERING PROPERTIES OF FILTERS
• Masas in the Calkin algebra without the Continuum Hypothesis
• Combinatorial Cardinal Characteristics of the Continuum
• Weak Distributivity, A Problem of Von Neumann and the Mystery of Measurability
• On partitions of the real line into compact sets
• Zapping Small Filters
• Parametrized $\diamondsuit $ principles
• COHERENT SYSTEMS OF FINITE SUPPORT ITERATIONS
• Ordering MAD families a la Katětov
• Set Theory
• The almost-disjointness number may have countable cofinality
• Borel’s conjecture and meager-additive sets
• RESTRICTED MAD FAMILIES
• Template iterations and maximal cofinitary groups
• Splitting, Bounding, and Almost Disjointness Can Be Quite Different
• α-Properness and Axiom A

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