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 \(MM^{++}\).
Original language | English |
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Title of host publication | >Computational prospects of infinity |
Subtitle of host publication | Part II: Presented Talks |
Place of Publication | Singapore |
Publisher | World Scientific Publishing Co. Pte Ltd |
Pages | 23-46 |
Number of pages | 23 |
Volume | Lecture Notes Series 15 |
ISBN (Electronic) | 978-981-4471-52-7 |
ISBN (Print) | 978-981-279-654-7 |
Publication status | Published - 2008 |