**Background/motivation:** A model for the **classical** propositional calculus is a boolean function *b(S)* which assigns 1 or 0 to each (modal-free) sentence *S* according to the usual rules. I'm looking at models for propositional **modal** logic, where a modal model is simply a collection of classical models as points. These simplified models make no use of a relation R that holds between points, nor of any one point as designated. How many modal models are there? I have two answers:

1) There are continuously many (*c*) classical models. Since any subset of the collection of classical models is a modal model, there are *(2^c) > c* modal models.

2) Suppose that for any given collection *B* = {*b1*, *b2*, ...} of classical models, the product of the collection *B* is defined as a function *f(S)* such that for each sentence *S*:

*f(S)*= 1 iff*bi(S)*= 1 for all*bi*∈ B;*f(S)*= 0 iff*bi(S)*= 0 for all*bi*∈ B;*f(S)*= -1 otherwise.

Since the function *f(S)* has a countable infinity of inputs and only finitely many outputs, it appears there are continuously many such functions. (Perhaps this assumes AC?)

The two answers can be reconciled if two different collections *B1* and *B2* of classical models both define the same function *f(S)*. But I don't see how that's possible. So there's something I'm missing.