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Two applications of finite side conditions at \(\omega _2\)

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Abstract

We present two applications of forcing with finite sequences of models as side conditions, adding objects of size \(\omega _2\). The first involves adding a \(\Box _{\omega _1}\) sequence and variants of such sequences. The second involves adding partial weak specializing functions for trees of height \(\omega _2\).

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Authors and Affiliations

  1. Department of Mathematics, University of California Los Angeles, Los Angeles, CA, 90095-1555, USA

    Itay Neeman

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  1. Itay Neeman
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Correspondence to Itay Neeman.

Additional information

This material is based upon work supported by the National Science Foundation under Grants No. DMS-1101204 and DMS-1363364, and the Simons Foundation under Simons Fellowship No. 225854.

The material from Definition 3.26 to the end of Section 3 was added in revision in July 2015.

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Neeman, I. Two applications of finite side conditions at \(\omega _2\) . Arch. Math. Logic 56, 983–1036 (2017). https://doi.org/10.1007/s00153-017-0550-y

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  • DOI: https://doi.org/10.1007/s00153-017-0550-y

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