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 (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	Pure Connector
Date Deposited:	01 Nov 2013 13:58
Last Modified:	07 Nov 2024 12:37
URI:	https://ueaeprints.uea.ac.uk/id/eprint/44050
DOI:	10.1016/j.apal.2007.02.002

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