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Inferences Over Fields: A Preliminary Investigation into the Deductive Capabilities of Field-Theoretically Defined Logical Connectives
(East Carolina University, 2023-05-03)
In this paper, we will be concerned with developing an inferential structure over the field with four elements in characteristic $2$. We begin by discussing the historical context in which this research occurs. In subsequent ...
First Order Definition of Rings Using Group of Units
(East Carolina University, 2023-05-03)
We discuss the technical background and relevant research regarding the undecidability of $O_{\mathbb{Q}^{\text{ab}}}$. Given an algebraic extension $K/\mathbb{Q}$, we consider the subring defined by
$$R_K=\{x\in O_K\,|\,\forall ...