Coding with canonical functions

Paul B. Larson; Saharon Shelah

doi:10.1002/malq.201500060

Coding with canonical functions

Paul B. Larson^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

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

Abstract

A function f from ω₁ to the ordinals is called a canonical function for an ordinal α if f represents α in any generic ultrapower induced by forcing with ℘(ω₁)/NS_ω1.We introduce here a method for coding sets of ordinals using canonical functions from ω₁ to ω₁. Combining this approach with arguments from [3], we show, assuming the Continuum Hypothesis, that for each cardinal κ there is a forcing construction preserving cardinalities and cofinalities forcing that every subset of κ is an element of the inner model L(℘(ω₁)).

Original language	English
Pages (from-to)	334-341
Number of pages	8
Journal	Mathematical Logic Quarterly
Volume	63
Issue number	5
DOIs	https://doi.org/10.1002/malq.201500060
State	Published - Dec 2017

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© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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Coding with canonical functions

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