REU Project

Large cardinal axioms postulate the existence of combinatorial properties of infinity. These axioms are far beyond the usual axioms of mathematics and expand the burden of the mathematical universe. A well-studied consequence of large cardinal axioms is compactness. Compactness denotes the extent to which mathematical structures are determined by their local behavior. In this project we continued the study of compactness properties for algebraic structures. We proved two compactness theorems in the context of almost projective modules from lambda-strongly compact and weakly compact, respectively.