Department of Mathematics
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What sorts of properties can be expressed in infinitary languages for modules? If we mean properties which genuinely need infinitary languages, the obvious answer is "only complicated and obscure ones".

Jointly with Dr. Ph. Rothmaler of the City University of New York, I am studying various aspects of the infinitary logic of modules, in particular those properties which can be expressed by infinitary positive primitive formulas, and with a focus on various kinds of duality for these properties. We are very interested in finding specific (algebraic) illustrations and applications of our theorems.

We define a concept of "closure of a property with respect to a decreasing sequence of properties", motivated by ideas from the p-adic construction. I show how this property can be expressed by an infinitary pp formula, and calculate (and attempt to interpret) its syntactic dual.