# Sh:1076

• Larson, P. B., & Shelah, S. (2017). Coding with canonical functions. MLQ Math. Log. Q., 63(5), 334–341.
• Abstract:
A function f from \omega_{1} to the ordinals is called a canonical function for an ordinal \alpha if f represents \alpha in any generic ultrapower induced by forcing with \mathcal{P}(\omega_{1})/\mathrm{NS}_{\omega_{1}}. We introduce here a method for coding sets of ordinals using canonical functions from \omega_{1} to \omega_{1}. Combining this approach with arguments from [Sh:f], we show that for each cardinal \kappa there is a forcing construction preserving cardinalities and cofinalities forcing that every subset of \kappa is in the inner model L(\mathcal{P}(\omega_{1})).
• Version 2016-06-07_11 (12p) published version (8p)
Bib entry
@article{Sh:1076,
author = {Larson, Paul B. and Shelah, Saharon},
title = {{Coding with canonical functions}},
journal = {MLQ Math. Log. Q.},
fjournal = {MLQ. Mathematical Logic Quarterly},
volume = {63},
number = {5},
year = {2017},
pages = {334--341},
issn = {0942-5616},
mrnumber = {3748478},
mrclass = {03E35},
doi = {10.1002/malq.201500060}
}