On the existence of independent axiom systems for infinite sentence systems -- On the relation between intuitionist and classical arithmetic -- Investigations into logical deduction -- Consistency of elementary number theory -- Consistency of the simple theory of types -- Concept of infinity in mathematics -- Present state of research into the foundations of mathematics -- New version of the consistency proof for elementary number theory -- Provability and nonprovability of restricted transfinite induction in elementary number theory -- Fusion of several complete inductions.