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 extend a result of Ding and Helleseth on the autocorrelation of a cyclotomic generator in several ways. We define and analyze cyclotomic generators of arbitrary orders and over arbitrary finiteâ€¦ (More)

We study the reverse mathematics and computability of countable graph theory, obtaining the following results. The principle that every countable graph has a connected component is equivalent to ACA0â€¦ (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)

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)

Matroids generalize the familiar notion of linear dependence from linear algebra. Following a brief discussion of founding work in computability and matroids, we use the techniques of reverseâ€¦ (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)