Lectures on proof theory -- Partitions and models -- Klassen rekursiver funktionen -- Hyperarithmetic ultrafilters -- Recursive equivalence: A survey -- Half-ring morphologies -- Formalisations of some ?0 ?ukasiewicz propositional calculi -- Theories which are not ?o-categorical -- The monadic fragment of predicate calculus with the Chang quantifier and equality -- The ? 1 1 -comprehension schema and ?-rules.