Epimorphism Surjectivity in Logic and Algebra

Abstract

As the theorems we aim to prove require a variety of tools and background theory, we will start by recalling some basics of first-order logic (Section 2.1), model theory (Section 2.2), and universal algebra (Section 2.3). We will then continue presenting the protagonist of this thesis, the epimorphism surjectivity property, and making some easy but useful observations concerning this property (Section 2.4). Finally, we will establish a correspondence between the (weak) ES property in algebra and the (finite) Beth definability property in logic, providing motivation for the study of the ES property from a logical standpoint (Section 2.5)