The Journal of Symbolic Logic

Research Article

The complexity of continuous embeddability between dendrites

Alberto Marconea1 and Christian Rosendala2

a1 Dipartimento di Matematica e Informatica, Università di Udine, Via Delle Scienze 208, 33100 Udine, Italy, E-mail:

a2 Équipe D'Analyse Fonctionnelle, Université Paris 6, Tour 46-0. Boîte 186; 4, Place Jussieu, 75252 Paris, France, E-mail:


We show that the quasi-order of continuous embeddability between finitely branching dendrites (a natural class of fairly simple compacta) is -complete. We also show that embeddability between countable linear orders with infinitely many colors is -complete.

(Received May 25 2003)

(Revised January 16 2004)