Hybrid Definability in Topological Spaces
Dmitry Sustretov
Abstract:
We present some results concerning definability of classes of
topological spaces in hybrid languages. We use language $L_t$
described in Flum and Ziegler's monograph "Topological Model Theory"
to establish notion of ``elementarity'' for classes of topological
spaces. We use it to prove the analogue of Goldblatt-Thomason theorem
in topological spaces for hybrid languages $H(E)$ and $H(@)$. We also
prove a theorem that allows to reformulate definability result of
Gabelaia for modal logic in terms of elementary topological space
classes.
Keywords: hybrid logic, topology, definability, correspondence