Guessing and non-guessing of canonical functions

Asperó, D. (2007) Guessing and non-guessing of canonical functions. Annals of Pure and Applied Logic, 146 (2-3). pp. 150-179. ISSN 0168-0072

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Abstract

It is possible to control to a large extent, via semiproper forcing, the parameters (ß, ß) measuring the guessing density of the members of any given antichain of stationary subsets of ? (assuming the existence of an inaccessible limit of measurable cardinals). Here, given a pair (ß, ß) of ordinals, we will say that a stationary set S ? ? has guessing density (ß, ß) if ß = ? (S) and ß = sup {? (S) : S ? S, S stationary}, where ? (S) is, for every stationary S ? ?, the infimum of the set of ordinals t = ? + 1 for which there is a function F : S {long rightwards arrow} P (?) with o t (F (?)) <t for all ? ? S and with {? ? S : g (?) ? F (?)} stationary for every a <? and every canonical function g for a. This work involves an analysis of iterations of models of set theory relative to sequences of measures on possibly distinct measurable cardinals. As an application of these techniques I show how to force, from the existence of a supercompact cardinal, a model of PFA in which there is a well-order of H (?) definable, over <H (?), ? >, by a formula without parameters.

Item Type: Article
Uncontrolled Keywords: guessing canonical functions,iterations relative to sequences of measures on cardinals,pfa++,definable well-orders of h(ω2)
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: Pure Connector
Date Deposited: 01 Nov 2013 13:58
Last Modified: 21 Apr 2020 22:05
URI: https://ueaeprints.uea.ac.uk/id/eprint/44050
DOI: 10.1016/j.apal.2007.02.002

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