On variants of the principle of consistent choices, the minimal cover property and the 2-compactness of generalized Cantor cubes

In set theory without the Axiom of Choice (AC), we study the deductive strength of variants of the Principle of Consistent Choices (PCC) and their relationship with the minimal cover property, the 2-compactness of generalized Cantor cubes, and with certain weak choice principles. (Complete definitions are given in Section “Notation and terminology”.) Among other results, we establish the following: