  Inspired by the theory of desirable gambles that is used to model uncertainty
in the field of imprecise probabilities, I present a theory of desirable
things. Its aim is to model a subject's beliefs about which things are
desirable. What the things are is not important, nor is what it means for them
to be desirable. It can be applied to gambles, calling them desirable if a
subject accepts them, but it can just as well be applied to pizzas, calling
them desirable if my friend Arthur likes to eat them. Other useful examples of
things one might apply this theory to are propositions, horse lotteries, or
preferences between any of the above. Regardless of the particular things that
are considered, inference rules are imposed by means of an abstract closure
operator, and models that adhere to these rules are called coherent. I consider
two types of models, each of which can capture a subject's beliefs about which
things are desirable: sets of desirable things and sets of desirable sets of
things. A crucial result is that the latter type can be represented by a set of
the former.
