## Yde Venema

Institute for Logic

Language and Computation

University of Amsterdam

Plantage Muidergracht 24

1018 TV Amsterdam

yde@wins.uva.nl

http://www.wins.uva.nl/~yde

### Abstract

We give a structural characterization of those classes of modal models and of pointed modal models that are definable using a set of modal formulas. This characterization is new (as far as I know) in the sense that it only refers to modal notions such as bisimulations and ultrafilter extensions. The paper is entirely self-contained.

### Further Information

When I took my first class in modal logic with Johan van Benthem (this is about fifteen years ago), already in the first lecture he was discussing the standard translation and correspondence theory. The van Benthem style of studying modal logic in close connection with other branches of logic has proven to be very fruitful and influential. As a little teaser, I tried to write a paper on modal logic which mentions no first order logic or universal algebra, and in which Johan is not mentioned in the introduction.

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