Coding with canonical functions

Mathematical Logic Quarterly 63 (5):334-341 (2017)
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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 math formula. We introduce here a method for coding sets of ordinals using canonical functions from ω1 to ω1. Combining this approach with arguments from, 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 math formula.



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The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
Proper and Improper Forcing.Péter Komjáath - 2000 - Studia Logica 64 (3):421-425.

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