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

## 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 |
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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 |

UEA Research Groups: | Faculty of Science > Research Groups > Logic |

Related URLs: | |

Depositing User: | Pure Connector |

Date Deposited: | 01 Nov 2013 13:58 |

Last Modified: | 24 Oct 2022 04:54 |

URI: | https://ueaeprints.uea.ac.uk/id/eprint/44050 |

DOI: | 10.1016/j.apal.2007.02.002 |

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