# On the spectra of cardinalities of branches of Kurepa trees

## TL;DR

This paper investigates the possible sets of branch cardinalities in Kurepa trees within models of ZFC + CH, providing conditions under which these sets can be realized consistently.

## Contribution

It introduces a sufficient condition for sets of cardinals to be the branch cardinalities of Kurepa trees in certain models.

## Key findings

- Identifies conditions for sets of cardinals to correspond to branch sizes in Kurepa trees.
- Provides a method to realize these sets consistently in models of ZFC + CH.
- Advances understanding of the structure of Kurepa trees in set theory.

## 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.