{{menu|Teaching|Selected topics in mathematical logic}}
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Time: Tue, Thu 2:00pm–3:00pm<br/>
starts 2016&#8209;03&#8209;01<br/>
Place: KGRC

In this course I'll explore three central combinatorial properties of set theory and their interaction. The Tree Property (TP) at a regular cardinal $\kappa$ asserts
the nonexistence of a $\kappa$-tree with no $\kappa$-branch. The Reflection Property (RP) at the successor $\kappa^+$ of a regular cardinal $\kappa$ asserts that any
stationary subset of $\kappa^+$ consisting of ordinals of cofinality less than $\kappa$ has a stationary proper initial segment. And the Approachability Property (AP)
at a regular cardinal $\kappa$ asserts the existence of a sequence $(a_i | i &lt; \kappa)$ of bounded subsets of $\kappa$ such that for club-many $\alpha &lt; \kappa$, there is a
cofinal sequence in $\alpha$ of ordertype cof$(\alpha)$ all of whose proper initial segments are of the form $a_i$ for some $i &lt; \alpha$. We'll develop the tools needed for
the "Eightfold Way Theorem", the result asserting that all 8 Boolean combinations of TP,RP,AP are possible at double successor cardinals. The situation at
successors of limit cardinals is not yet well-understood.