We show there is no categorical metric continuum. This means that for every
metric continuum X there is another metric continuum Y such that X and Y have
(countable) elementarily equivalent bases but X and Y are not homeomorphic. As
an application we show that the chainability of the pseudoarc is not a
first-order property of its lattice of closed sets.Comment: Revision after comments from referee (2006-01-16

Hart, Klaas Pieter