We prove that if a Î 2 sentence is provable in a certain theory of higher order arithmetic without the law of the excluded middle then it is uniformly provable in the weak classical theory RCA0.â€¦ (More)

We study the logical content of several maximality principles related to the finite intersection principle (F IP) in set theory. Classically, these are all equivalent to the axiom of choice, but inâ€¦ (More)

This is joint work with Carl Mummert. We initiate the reverse mathematics of general topology. We show that a certain metrization theorem is equivalent to Î 2 comprehension. An MF space is defined toâ€¦ (More)

If Nonempty has a winning strategy against Empty in the Choquet game on a space, the space is said to be a Choquet space. Such a winning strategy allows Nonempty to consider the entire finite historyâ€¦ (More)

We study two classes of spaces whose points are filters on partially ordered sets. Points in MF spaces are maximal filters, while points in UF spaces are unbounded filters. We give a thorough accountâ€¦ (More)

We study the reverse mathematics of the principle stating that, for every property of finite character, every set has a maximal subset satisfying the property. In the context of set theory, thisâ€¦ (More)

Let n be a positive integer. By a Î²n-model we mean an Ï‰-model which is elementary with respect to Î£n formulas. We prove the following Î²n-model version of GÃ¶delâ€™s Second Incompleteness Theorem. Forâ€¦ (More)

We explore the problem of constructing maximal and unbounded filters on computable posets. We obtain both computability results and reverse mathematics results. A maximal filter is one that does notâ€¦ (More)