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

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review


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 \(MM^{++}\).
Original languageEnglish
Title of host publication>Computational prospects of infinity
Subtitle of host publicationPart II: Presented Talks
Place of PublicationSingapore
PublisherWorld Scientific Publishing Co. Pte Ltd
Number of pages23
VolumeLecture Notes Series 15
ISBN (Electronic)978-981-4471-52-7
ISBN (Print) 978-981-279-654-7
Publication statusPublished - 2008

Cite this