On non-wellfounded iterations of the perfect set forcing

DOI10.2307/2586484zbMath0930.03062OpenAlexW2095873474MaRDI QIDQ4262569

Kanovei, Vladimir

Publication date: 12 September 1999

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2586484

zbMATH Keywords

iterated forcingcardinal invariantSacks forcinggeneric extensiongeneric modeldegrees of constructibilitytransitive modelBurgess selection principle for analytic equivalence relationsiterated Sacks extensionsproduct extensionsSacks generic reals

Mathematics Subject Classification ID

Other aspects of forcing and Boolean-valued models (03E40)

Related Items (12)

Models of set theory in which the separation theorem fails ⋮ The full basis theorem does not imply analytic wellordering ⋮ Canonization of smooth equivalence relations on infinite-dimensional \(\mathsf{E}_0\)-large products ⋮ Inner mantles and iterated HOD ⋮ 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 ⋮ Factoring Solovay-random extensions, with application to the reduction property ⋮ Forcing indestructibility of MAD families ⋮ On coding uncountable sets by reals ⋮ A weak dichotomy below \(\mathrm{E}_1\times\mathrm{E}_3\) ⋮ ISOLATING CARDINAL INVARIANTS ⋮ Pyramidal structure of constructibility degrees ⋮ Saccharinity

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