Vol. 311, No. 2, 2021

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Characterizing the spectra of cardinalities of branches of Kurepa trees

Márk Poór and Saharon Shelah

Vol. 311 (2021), No. 2, 423–453
Abstract

We give a complete characterization of the sets of cardinals that in a suitable forcing extension can be the Kurepa spectrum, that is, the set of cardinalities of branches of Kurepa trees. This answers a question of Poór.

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Keywords
Kurepa tree, constructible universe, cardinal spectra
Mathematical Subject Classification 2010
Primary: 03E35
Secondary: 03E05, 03E45
Milestones
Received: 23 March 2020
Revised: 5 December 2020
Accepted: 9 December 2020
Published: 31 July 2021
Authors
Márk Poór
Institute of Mathematics
Eötvös Loránd University, Budapest
Budapest
Hungary
Saharon Shelah
Einstein Institute of Mathematics
The Hebrew University of Jerusalem, Edmond J Safra Campus
Jerusalem
Israel
Department of Mathematics
Rutgers, The State University of New Jersey
Piscataway, NJ
United States