Konstruktivität und logische Komplexität in Arithmetik und Mengenlehre

• Applicant: Dr. Wolfgang Burr
• Subject Area: Mathematics
• Term: from 2000 to 2003
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5276193

Arithmetic and set theory are of fundamental importance for the foundations of mathematics and have been studied intensively over the past decades. Complexity and constructivity play an important role in this field of research: one is interested in the proof-theoretic complexity of mathematical theories, in their computational complexity, in properties of intuitionistic systems whose presence underlines their constructive character and in the relation between classical and intuitionistic theories.The principal object of my project is to obtain a better understanding of the notion of constructivity. Therefore I intend to work out measures that characterize not only the mathematical strength of a theory - as proof theory usually does - but also its logical strength. In the intuitionistic context the question of logical complexity has not been systematically adressed so far. Hence, many questions that have long been answered for classical systems are left open for intuitionistic and constructive ones. My aim is to close this obvious gap in our knowledge and to systematically approach the study of intuitionistic theories from the point of view of logical complexity.

• DFG Programme: Emmy Noether International Fellowships