Fresh logic: Proof-theory and semantics for FM and nominal techniques (Q2372191)

In this paper a formal framework, called fresh logic, is introduced and studied with respect to its semantics and proof theory. The logic originates from Fraenkel-Mostowski set theory featuring a quantifier И `for all but a finite set of names'. The aim of the author is to provide ``a logic whose judgements look like normal first-order logic, whose language is augmented with the FM И-quantifier, and with a good proof theory and semantics'' (p.~357).