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On the spectra of cardinalities of branches of Kurepa trees

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Abstract

We are interested in the possible sets of cardinalities of branches of Kurepa trees in models of ZFC \(+\) CH. In this paper we present a sufficient condition (for sets of cardinals) to be consistently the set of cardinalities of branches of Kurepa trees.

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Acknowledgements

I would like to thank my masters thesis supervisor Péter Komjáth for presenting me the problem, and also giving hints and ideas, providing some useful advice.

I also gratefully thank to the referee for constructive comments and recommendations, also pointing to possible simplifications of otherwise tedious technical arguments.

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  1. Institute of Mathematics, Eötvös Loránd University, Pázmány Péter s. 1/c, Budapest, 1117, Hungary

    Márk Poór

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  1. Márk Poór
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Correspondence to Márk Poór.

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The author was supported by the National Research, Development and Innovation Office - NKFIH, Grant Nos. 104178, 124749 and 129211. Supported by the ÚNKP-18-3 New National Excellence Program of the Ministry of Human Capacities.

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Poór, M. On the spectra of cardinalities of branches of Kurepa trees. Arch. Math. Logic 60, 927–966 (2021). https://doi.org/10.1007/s00153-021-00767-6

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  • DOI: https://doi.org/10.1007/s00153-021-00767-6

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