# Sh:1076

- Larson, P. B., & Shelah, S. (2017).
*Coding with canonical functions*. MLQ Math. Log. Q.,**63**(5), 334–341. DOI: 10.1002/malq.201500060 MR: 3748478 -
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} }