Hybrid Definability in Topological Spaces

Abstract : We present some results concerning the definability of classes of topological spaces in hybrid languages. We use the language $L_t$ described in Flum and Ziegler's monograph "Topogical Model Theory" to establish the notion of "elementarity'' for classes of topological spaces. We use it to prove the analogue of the Goldblatt-Thomason theorem in topological spaces for hybrid languages $H(E)$ and $H(@)$. We also prove a theorem that allows us to reformulate the definability result of Gabelaia (given in his Mater's thesis) for modal logic in terms of elementary topological space classes.