Partition Theorems for Spaces of Variable Words

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135422/1/plms0449.pd

Reverse Mathematics of Ramsey\u27s Theorem

Reverse mathematics aims to determine which set theoretic axioms are necessary to prove the theorems outside of the set theory. Since the 1970’s, there has been an interest in applying reverse mathematics to study combinatorial principles like Ramsey’s theorem to analyze its strength and relation to other theorems. Ramsey’s theorem for pairs states that for any infinite complete graph with a finite coloring on edges, there is an infinite subset of nodes all of whose edges share one color. In this thesis, we introduce the fundamental terminology and techniques for reverse mathematics, and demonstrate their use in proving Kőnig\u27s lemma and Ramsey\u27s theorem over RCA0

A consistent conditional moment test of functional form

Conditional moment (CM) tests of functional form exploit the property that for correctly specified models the conditional expectation of certain functions of the observations should be almost surely equal to zero. A chi-square misspecification test can then be based on weighted means of thes

CANONICAL FORMS OF BOREL FUNCTIONS ON THE MILLIKEN SPACE

ABSTRACT: The goal of this paper is to canonize Borel measurable mappings , where is the Milliken space, i.e., the space of all increasing infinite sequences of pairwise disjoint nonempty finite sets of . Our main result refers to the metric topology on the Milliken space. The result is a common generalization of a theorem of Taylor (cf. Theorem 0.4) and a theorem of Prömel and Voigt (cf. Theorem 0.7)