UCI and Entrepreneurship, Blog 3

Student blog posts from the Great VCU Bike Race Book

Amalgam Fillings: Do Dental Patients Have a Right to Informed Consent

Recent animal studies have shown significant mercury absorption from dental fillings and resulted in unfavorable media attention. Yet, an FDA advisory committee has found no evidence of Risk to dental patients, and many dentists believe that patients are being unnecessarily alarmed. The paper reviews the history of amalgam fillings through the recent animal studies and concludes that the Risk, whatever it may prove to be, is sufficiently high to warrant permitting patients to choose between amalgam and alternative dental filling materials

Positronium lifetime in polymers

A model describing the relationship between the ortho--positronium lifetime and the volume of a void, located in a synthetic zeolite, is analyzed. Our idea, which allows us to take into account the effects of temperature, comprises the introduction of a non--hermitian term in the Hamiltonian, which accounts for the annihilation of the ortho--positronium. The predictions of the present model are also confronted against an already known experimental result.Comment: Accepted in Journal of Chemical Physic

Classical Predicative Logic-Enriched Type Theories

A logic-enriched type theory (LTT) is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named LTTO and LTTO*, which we claim correspond closely to the classical predicative systems of second order arithmetic ACAO and ACA. We justify this claim by translating each second-order system into the corresponding LTT, and proving that these translations are conservative. This is part of an ongoing research project to investigate how LTTs may be used to formalise different approaches to the foundations of mathematics. The two LTTs we construct are subsystems of the logic-enriched type theory LTTW, which is intended to formalise the classical predicative foundation presented by Herman Weyl in his monograph Das Kontinuum. The system ACAO has also been claimed to correspond to Weyl's foundation. By casting ACAO and ACA as LTTs, we are able to compare them with LTTW. It is a consequence of the work in this paper that LTTW is strictly stronger than ACAO. The conservativity proof makes use of a novel technique for proving one LTT conservative over another, involving defining an interpretation of the stronger system out of the expressions of the weaker. This technique should be applicable in a wide variety of different cases outside the present work.Comment: 49 pages. Accepted for publication in special edition of Annals of Pure and Applied Logic on Computation in Classical Logic. v2: Minor mistakes correcte