A restricted second order logic for finite structures

Team logic is a new logic, introduced by Väänänen [12], extending dependence logic by classical negation. Dependence logic adds to first-order logic atomic formulas expressing functional dependence of variables on each other. It is known that on the ...

We extend universal algebra and its equational logic from first to second order as follows. 1. We consider second-order equational presentations as specified by identities between second-order terms, with both variables and parameterised metavariables ...

An operation M* which constructs from a given structure M a tree-like structure whose domain consists of the finite sequences of elements of M is considered. A notion of automata running on such tree-like structures is defined. It is shown that automata ...