Lehrveranstaltungsleiter: Alexander Leitsch
Diese Lehrveranstaltung ist Wahlfach im Magisterstudium Computational Intelligence
(Bereich "Diskrete Mathematik und Logik").
This course also belongs to the advanced modules Logical foundations and Inference in classical and nonclassical logics of the international Master Programme in Computational Logic.
Monday October 10, 2:00 p.m.
Main Building, Karlsplatz 13
Basic Principles of Second-Order Logic:
Second-order logic differs from first-order one in admitting predicate variables. This extension adds substantial expressive power to the language. We show that number theory is (non-effectively) axiomatizable by second-order axioms and that, as a consequence, second-order logic is not mechanizable. On the proof theoretic side we introduce a second-order Gentzen system LK2 and second-order arithmetic. We show that induction can be expressed in LK2 making it stronger than Peano arithmetic.