A minimal model for -xh: Iteration of jensen’s reals

Uri Abraham

doi:10.1090/S0002-9947-1984-0722767-0

A minimal model for -xh: Iteration of jensen’s reals

Uri Abraham

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

A model of ZFC + 2^N₀ = N₂ is constructed which is minimal with respect to being a model of CH. Any strictly included submodel of ZF (which contains all the ordinals) satisfies CH. In this model the degrees of constructibility have order type ω₂. A novel method of using the diamond is applied here to construct a countable-support iteration of Jensen’s reals: In defining the ath stage of the iteration the diamond “guesses” possible β > α stages of the iteration.

Original language	English
Pages (from-to)	657-674
Number of pages	18
Journal	Transactions of the American Mathematical Society
Volume	281
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1984-0722767-0
State	Published - 1 Jan 1984

ASJC Scopus subject areas

Mathematics (all)
Applied Mathematics

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AB - A model of ZFC + 2N0 = N2 is constructed which is minimal with respect to being a model of CH. Any strictly included submodel of ZF (which contains all the ordinals) satisfies CH. In this model the degrees of constructibility have order type ω2. A novel method of using the diamond is applied here to construct a countable-support iteration of Jensen’s reals: In defining the ath stage of the iteration the diamond “guesses” possible β > α stages of the iteration.

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A minimal model for -xh: Iteration of jensen’s reals

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