Few new reals

David Aspero; Miguel Angel Mota

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arXiv · 1712.07724

Few new reals

David Aspero·Miguel Angel Mota

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Abstract

We introduce a new method for building models of CH, together with $Π_2$ statements over $H(ω_2)$, by forcing. Unlike other forcing constructions in the literature, our construction adds new reals, although only $\aleph_1$-many of them. Using this approach, we build a model in which a very strong form of the negation of Club Guessing at $ω_1$ 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.

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BibTeX RIS

David Aspero, Miguel Angel Mota. 2023-03-21. Few new reals. https://arxiv.org/abs/1712.07724

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