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Fake reflection

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Abstract

We introduce a generalization of stationary set reflection which we call filter reflection, and show it is compatible with the axiom of constructibility as well as with strong forcing axioms. We prove the independence of filter reflection from ZFC, and present applications of filter reflection to the study of canonical equivalence relations over the higher Cantor and Baire spaces.

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Acknowledgements

This research was partially supported by the European Research Council (grant agreement ERC-2018-StG 802756). The third author was also partially supported by the Israel Science Foundation (grant agreement 2066/18). At the end of the preparation of this article, the second author was visiting the University of Vienna supported by the Vilho, Yrjö and Kalle Väisälä Foundation of the Finnish Academy of Science and Letters.

We thank Andreas Lietz, Benjamin Miller, Ralf Schindler and Liuzhen Wu for their feedback on a preliminary version of this manuscript.

We are deeply grateful to the anonymous referee for their corrections, comments and improvements. Most notably, the second part of the proof of Claim 5.4.2 is due to them, and enabled to waive the initial hypothesis that X and S are disjoint.

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Authors and Affiliations

  1. Department of Mathematics, Bar-Ilan University, Ramat-Gan, 5290002, Israel

    Gabriel Fernandes, Miguel Moreno & Assaf Rinot

  2. Institute of Mathematics, University of Vienna, Vienna, 1090, Austria

    Miguel Moreno

Authors
  1. Gabriel Fernandes
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  2. Miguel Moreno
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  3. Assaf Rinot
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Correspondence to Assaf Rinot.

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Fernandes, G., Moreno, M. & Rinot, A. Fake reflection. Isr. J. Math. 245, 295–345 (2021). https://doi.org/10.1007/s11856-021-2213-2

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  • DOI: https://doi.org/10.1007/s11856-021-2213-2

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