Tarski's truth as a local metalinguistic predicate

I will argue that the more advanced semantic paradoxes do not cause any trouble with Tarski's solution to the liar paradox, i.e. drawing a hierarchical picture of language, but that they even go further to provide guidance for discovering the true structure of metalanguage. Paradoxes arise when we presuppose a global layered structure for language. Metalanguage should not be considered as the upper layer of language, but rather as a defined topology on object language, which allows for a variety of hierarchical structures. In this more exact picture of metalanguage, Tarski's conception of truth must be construed as a local one, i.e. truth as a local predicate. This approach may shed some light on the less explored aspects of semantic paradoxes, especially Yablo's paradox. I will discuss that by considering a circular topology, a non-self-referential and non-paradoxical model can be obtained to locally attribute truth and falsehood to Yablo's expressions.