The complexity of continuous embeddability between dendrites

Abstract. We show that the quasi-order of continuous embeddability between Þnitely branching den-drites (a natural class of fairly simple compacta) is ¶11-complete. We also show that embeddability between countable linear orders with inÞnitely many colors is ¶11-complete. x1. Introduction. In [LR02] Louveau and Rosendal initiated the study of the complexity of ¶11 (i.e., analytic) quasi-orders on Polish (i.e., separable and com-pletely metrizable) spaces. This study yields results about the complexity of the equivalence relation induced by the quasi-order and thus contributes to the on-going study of analytic equivalence relations. The equivalence relations obtaine