On November 6, 2025, at 14:00 EET, Ionuț Țuțu (Institute of Mathematics of the Romanian Academy) will give a talk in the Logic Seminar.
Title: Forcing, Transition Algebras, and Calculi
Abstract:
We introduce a logic of transition algebras that enhances many-sorted first-order logic with features commonly found in dynamic logics. This brings a significantly higher degree of expressivity, allowing us to axiomatize properties such as finiteness or reachability. We discuss syntactic entailment, study basic properties such as compactness and completeness, and show that the latter does not hold under standard finitary proof rules. Consequently, we define proof rules having both finite and countably infinite premises, and we provide conditions under which completeness can be proved. To wrap up, we further develop the forcing method introduced in model theory by Abraham Robinson and we demonstrate its use in order to obtain a completeness result for signatures that are at most countable. This is joint work with Go Hashimoto and Daniel Găină.
The talk will take place physically at FMI (the new PBTower location), Hall 102.