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.