Few new reals

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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
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 Engineering, Mathematics and Physics
UEA Research Groups: Faculty of Science > Research Groups > Logic (former - to 2024)
Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Related URLs:
Depositing User: LivePure Connector
Date Deposited: 15 May 2024 13:31
Last Modified: 07 Nov 2024 12:47
URI: https://ueaeprints.uea.ac.uk/id/eprint/95210
DOI: 10.1142/S0219061323500095

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