Date of Award
8-1-2026
Degree Name
Master of Science
Department
Mathematics
First Advisor
Calvert, Wesley
Abstract
In non-classical logic, one often observes that concepts which were previously equivalent or even did not need to be explicated suddenly split apart and become more complicated. Here, following the work of Badia and Tedder , I study the theory of vector spaces over the rationals over logics between B and RM. In particular, we see that this theory no longer enjoys such properties as quantifier elimination and strong minimality. Furthermore, unlike in the classical case, this theory has continuum many non-isomorphic countable models and is in fact unstable.
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