SELECTIVE INDEPENDENCE AND $h$-PERFECT TREE FORCING NOTIONS (Recent Developments in Set Theory of the Reals)

SELECTIVE INDEPENDENCE AND $h$-PERFECT TREE FORCING NOTIONS (Recent Developments in Set Theory of the Reals)

descriptionPublicationkeyboard_double_arrow_right Article English Journal:SELECTIVE INDEPENDENCE AND $h$-PERFECT TREE FORCING NOTIONS (Recent Developments in Set Theory of the Reals), volume 2,213, pages 63-73 (issn: 1880-2818,

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SELECTIVE INDEPENDENCE AND $h$-PERFECT TREE FORCING NOTIONS (Recent Developments in Set Theory of the Reals)

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Abstract

Generalizing the proof for Sacks forcing, we show that the h-perfect tree forcing notions introduced by Goldstern, Judah and Shelah preserve selective independent families even when iterated. As a result we obtain new proofs of the consistency of i= u < non(N) = cof(N) and i < u = non(N) = cof(N) as well as some related results.

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