Topics to be discussed include (A) the time and space hierarchy theorems and (B) alternation. If there is time we give a survey of the main inclusions between the different classes.
A set of printed notes will be made available to participants, including a summary of previous week's work.
Abstract: We will discuss topological set theory, a field concerned with the study of models of various set theories having interesting topological properties. Such models have been used (for example) to prove the consistency (relative to ZF) of the positive set theory GPK^+, which allows comprehension restricted to "positive" formulas. Towards the end we will discuss an attempt to construct similar models using nonstandard analysis applied to models of a subtheory of ZF.