Asperó, David and Mota, Miguel Angel (2024) Few new reals. Journal of Mathematical Logic (jml), 24 (02). ISSN 0219-0613
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Abstract
We introduce a new method for building models of CH, together with Π2 statements over H(ω2), by forcing. Unlike other forcing constructions in the literature, our construction adds new reals, although only ℵ1-many of them. Using this approach, we build a model in which a very strong form of the negation of Club Guessing at ω1 known as Measuring holds together with CH, thereby answering a well-known question of Moore. This construction can be described as a finite-support weak forcing iteration with side conditions consisting of suitable graphs of sets of models with markers. The CH-preservation is accomplished through the imposition of copying constraints on the information carried by the condition, as dictated by the edges in the graph.
Item Type: | Article |
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Uncontrolled Keywords: | ch-preservasion,measuring,side conditions,adding reals,ch-preservation,logic ,/dk/atira/pure/subjectarea/asjc/2600/2609 |
Faculty \ School: | Faculty of Science > School of Mathematics (former - to 2024) |
UEA Research Groups: | Faculty of Science > Research Groups > Logic |
Related URLs: | |
Depositing User: | LivePure Connector |
Date Deposited: | 15 May 2024 13:31 |
Last Modified: | 15 Aug 2024 00:41 |
URI: | https://ueaeprints.uea.ac.uk/id/eprint/95210 |
DOI: | 10.1142/S0219061323500095 |
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