A Minimal Degree Which Collapses $omega_1$

Journal of Symbolic Logic 49 (1):298-300 (1984)
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Abstract

We consider a well-known partial order of Prikry for producing a collapsing function of minimal degree. Assuming $MA + \neq CH$, every new real constructs the collapsing map

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Perfect tree forcings for singular cardinals.Natasha Dobrinen, Dan Hathaway & Karel Prikry - 2020 - Annals of Pure and Applied Logic 171 (9):102827.

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