Template iterations with non-definable ccc forcing notions

Abstract

We present a version with non-definable forcing notions of Shelah's theory of iterated forcing along a template. Our main result, as an application, is that, if $\kappa$ is a measurable cardinal and $\theta <\kappa <\mu <\lambda$ are uncountable regular cardinals, then there is a ccc poset forcing $\mathfrak{s}=\theta <\mathfrak{b}=\mu <\mathfrak{a}=\lambda$. Another application is to get models with large continuum where the groupwise-density number $\mathfrak{g}$ assumes an arbitrary regular value.

To appear in the Annals of Pure and Applied Logic, 45 pages, 2 figures

References in corpus (2)

• Matrix iterations and Cichon's diagram
• Models of some cardinal invariants with large continuum

Cited by in corpus (5)

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• Matrix iterations with vertical support restrictions
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