TY - JOUR
T1 - Coding with canonical functions
AU - Larson, Paul B.
AU - Shelah, Saharon
N1 - Publisher Copyright:
© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
PY - 2017/12
Y1 - 2017/12
N2 - 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)/NSω1.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)).
AB - 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)/NSω1.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)).
UR - http://www.scopus.com/inward/record.url?scp=85055096489&partnerID=8YFLogxK
U2 - 10.1002/malq.201500060
DO - 10.1002/malq.201500060
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AN - SCOPUS:85055096489
SN - 0942-5616
VL - 63
SP - 334
EP - 341
JO - Mathematical Logic Quarterly
JF - Mathematical Logic Quarterly
IS - 5
ER -