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arXiv · 2306.12831

Extender-based Magidor-Radin forcings without top extenders

Moti Gitik·Sittinon Jirattikansakul
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Abstract

Continuing \cite{GitJir22}, we develop a version of Extender-based Magidor-Radin forcing where there are no extenders on the top ordinal. As an application, we provide another approach to obtain a failure of SCH on a club subset of an inaccessible cardinal, and a model where the cardinal arithmetic behaviors are different on stationary classes, whose union is the club, is provided. The cardinals and the cofinalities outside the clubs are not affected by the forcings.

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Moti Gitik, Sittinon Jirattikansakul. 2023-06-22. Extender-based Magidor-Radin forcings without top extenders. https://arxiv.org/abs/2306.12831

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