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Square principles in ℙmax extensions

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Abstract

By forcing with Pmax over strong models of determinacy, we obtain models where different square principles at ω 2 and ω 3 fail. In particular, we obtain a model of \({2^{{\aleph _0}}} = {2^{{\aleph _1}}} = {\aleph _2} + {\neg }\square \left( {{\omega _2}} \right) + {\neg }\square \left( {{\omega _3}} \right)\) .

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Author information

Authors and Affiliations

  1. Mathematical Reviews, 416 Fourth Street, Ann Arbor, MI, 48103-4820, USA

    Andrés Eduardo Caicedo

  2. Department of Mathematics, Miami University, Oxford, OH, 45056, USA

    Paul Larson

  3. Department of Mathematics, Rutgers University, Hill Center for the Mathematical Sciences, 110 Frelinghuysen Rd., Piscataway, NJ, 08854-8019, USA

    Grigor Sargsyan

  4. Institut für mathematische Logik und Grundlagenforschung, Fachbereich Mathematik und Informatik, Universität Münster, Einsteinstraße 62, 48149, Münster, Germany

    Ralf Schindler

  5. Department of Mathematics, University of California at Berkeley, Berkeley, CA, 94720, USA

    John Steel

  6. Department of Mathematics, University of California at Irvine, Irvine, CA, 92697, USA

    Martin Zeman

Authors
  1. Andrés Eduardo Caicedo
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  2. Paul Larson
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  3. Grigor Sargsyan
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  4. Ralf Schindler
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  5. John Steel
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  6. Martin Zeman
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Correspondence to Andrés Eduardo Caicedo.

Additional information

Supported in part by AIM through a SQuaREs project.

The first author was also supported in part by NSF Grant DMS-0801189.

The second author was also supported in part by NSF Grants DMS-0801009 and DMS-1201494.

The third author was also supported in part by NSF Grants DMS-0902628, DMS-1201348 and DMS-1352034.

The fourth author gratefully acknowledges support from the SFB 878 of the Deutsche Forschungsgemeinschaft (DFG).

The fifth author was also supported in part by NSF Grant DMS-0855692. Received May 18, 2012 and in revised form December 7, 2015

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Caicedo, A.E., Larson, P., Sargsyan, G. et al. Square principles in ℙmax extensions. Isr. J. Math. 217, 231–261 (2017). https://doi.org/10.1007/s11856-017-1444-8

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  • DOI: https://doi.org/10.1007/s11856-017-1444-8

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