Notions of Independence: Examples and Properties - Bandeira, Bruno; Cerioli, Márcia R.; Viana, Petrucio (Anais do Workshop Brasileiro de Lógica (WBL); 2021: Anais do II Workshop Brasileiro de LógicaDO - 10.5753/wbl.2021.15775, 2021)
We analyze the notions of independence of a set of postulates, proposed by G. Peano, E. H. Moore, A. Church and F. Harary, together with a presumably new notion inspired by H. M. Sheffer. For each of these notions, we present a proper definition and give illustrative examples. We give a complete picture of the implications between these notions of independence. Then, we make some additional observations that shed some light on these notions and some concepts related to them.