Modal Correspondence Theory [PhD Thesis]

This is a doctoral dissertation of Johan van Benthem accomplished under the supervision of prof. Dr. M.H.Löb in 1976. This is one of the outstanding dissertations in modal logic. Later, J. van Benthem wrote a book "Modal Logic and Classical Logic", which is based on (and significantly extends) this dissertation. Cover ......Page 1 Acknowledgements ......Page 4 Table of contents ......Page 5 1. Introduction ......Page 6 2. Preliminary notions and results ......Page 20 3. An algebraic characterization of $overline{M}1$ ......Page 36 4. Syntactic results on M1 ......Page 46 5. Relative correspondence ......Page 72 6. Modal definability ......Page 80 References ......Page 116 1. A note on modal formulae and relational properties ......Page 120 1. Introduction ......Page 126 2. Preliminaries ......Page 127 3. MRPs on transitive frames ......Page 129 4. MRPs on frames with successors ......Page 133 5. MRPs on arbitrary frames ......Page 139 6. Some uses of MRPs ......Page 144 References ......Page 146 3. Modal formulas are either elementary or not $SigmaDelta$-elementary ......Page 148 Summary ......Page 152 Samenvatting ......Page 153 Stellingen behorend bij het proefschrift "Modal Correspondence Theory" van J.F.A.K. van Benthem ......Page 154