Glasnik Matematicki, Vol. 46, No.1 (2011), 7-10.

A NOTE ON ULTRAPRODUCTS OF VELTMAN MODELS

Mladen Vuković

Abstract.   We consider ultraproducts of Veltman models, and show that a version of Łos theorem is true.

2000 Mathematics Subject Classification.   03F45, 03B45.

Key words and phrases.   Interpretability logic, Veltman models, ultraproducts.

DOI: 10.3336/gm.46.1.02

References:

1. P. Blackburn, M. de Rijke and Y. Venema, Modal logic, Cambridge University Press, Cambridge, 2001.
   MathSciNet    

2. C. C. Chang, H. J. Keisler, Model theory, North-Holand, 1990.
   MathSciNet    

3. D. de Jongh, F. Veltman, Provability logics for relative interpretability, in: Mathematical Logic, Proceedings of the 1988 Heyting Conference, ed. P. P. Petkov, Plenum Press, New York, 1990, 31-42.
   MathSciNet    

4. V. Goranko, M. Otto, Model theory of modal logic, in: Handbook of Modal Logic, eds. F. Wolter et al., Elsevier, 2006.

5. G. Japaridze, D. de Jongh, The logic of provability, in: Handbook of Proof Theory, ed. S. R. Buss, Elsevier, 1998, 475-546.
   MathSciNet     CrossRef

6. A. Visser, An overview of interpretability logic, in: Advances in modal logic, Vol. 1 (Berlin, 1996), 307–359, CSLI Lecture Notes 87, CSLI Publ., Stanford, USA, 1998.
   MathSciNet    

7. D. Vrgoč, M. Vuković, Bisimulations and bisimulation quotients of generalized Veltman models, Logic Jou. IGPL 18 (2010), 870-880.
   CrossRef