Coding into \(H(\omega_2)\) together (or not) with forcing axioms. A survey

Aspero, David (2008) Coding into \(H(\omega_2)\) together (or not) with forcing axioms. A survey. In: >Computational prospects of infinity. World Scientific Publishing Co. Pte Ltd, Singapore, pp. 23-46. ISBN 978-981-279-654-7

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Abstract

This paper is mainly a survey of recent results concerning the possibility of building forcing extensions in which there is a simple definition, over the structure \(\langle H(\omega_2), \in\rangle\) and without parameters, of a prescribed member of $H(omega_2)$ or of a well--order of \(H(\omega_2)\). Some of these results are in conjunction with strong forcing axioms like \(PFA^{++}\) or \(MM\), some are not. I also observe (Corollary 4.4) that the existence of certain objects of size \(\aleph_1\) follows outright from the existence of large cardinals. This observation is motivated by an attempt to extend the \(PFA^{++}\) result to a result mentioning \(MM^{++}\).

Item Type:	Book Section
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
Depositing User:	Pure Connector
Date Deposited:	09 Jul 2014 12:06
Last Modified:	07 Nov 2024 12:49
URI:	https://ueaeprints.uea.ac.uk/id/eprint/49361
DOI:

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