Large continuum, oracles

Saharon Shelah

doi:10.2478/s11533-010-0018-3

Large continuum, oracles

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

2 Scopus citations

Abstract

Our main theorem is about iterated forcing for making the continuum larger than א₂. We present a generalization of [2] which deal with oracles for random, (also for other cases and generalities), by replacing א₁,א₂ by λ, λ⁺ (starting with λ = λ^<λ > א₁). Well, we demand absolute c. c. c. So we get, e.g. the continuum is λ⁺ but we can get cov(meagre) = λ and we give some applications. As in non-Cohen oracles [2], it is a "partial" countable support iteration but it is c. c. c.

Original language	English
Pages (from-to)	213-234
Number of pages	22
Journal	Central European Journal of Mathematics
Volume	8
Issue number	2
DOIs	https://doi.org/10.2478/s11533-010-0018-3
State	Published - Apr 2010

Keywords

Countable chain condition
Iterated forcing
Large continuum
Peculiar cuts

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10.2478/s11533-010-0018-3

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AB - Our main theorem is about iterated forcing for making the continuum larger than א2. We present a generalization of [2] which deal with oracles for random, (also for other cases and generalities), by replacing א1,א2 by λ, λ+ (starting with λ = λ<λ > א1). Well, we demand absolute c. c. c. So we get, e.g. the continuum is λ+ but we can get cov(meagre) = λ and we give some applications. As in non-Cohen oracles [2], it is a "partial" countable support iteration but it is c. c. c.

KW - Countable chain condition

KW - Iterated forcing

KW - Large continuum

KW - Peculiar cuts

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Large continuum, oracles

Abstract

Keywords

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