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The main abstract is repeated immediately following. Last week we covered most of the preliminary and background material. This week I will focus on the characterizations of Local Projectivity, including, if there is time, the translation of 'Property A' into an axiomatization by implications of infinitary pp formulas.

This will be a quite informal series of talks, exploring in some detail the algebraic aspects of the topics of the title. Philipp Rothmaler and I have an interesting application of some of our ideas on 'infinitary elementary duality', but don't understand the outcome in purely algebraic terms at all.

The hope is that by working through these details in front of an audience, we will resolve this difficulty. Along the way, you will see some standard techniques in module theory, and in the model theory of modules.

For an extended abstract, see this link