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Tree forcings and sharps
Author(s) -
Castiblanco Fabiana,
Schlicht Philipp
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610443
Subject(s) - statement (logic) , tree (set theory) , mathematics , climatology , mathematical economics , environmental science , philosophy , combinatorics , geology , epistemology
The Levy‐Solovay theorem and its variants show that various large cardinals are preserved under small forcings. We study the preservation of consequences of large cardinals under proper forcings. In particular, we consider the preservation of the statement that every real has a sharp for classical tree forcings. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)