 There are several approaches to set theory with naive comprehension via paraconsistent logic. Models for paraconsistent set theory are described by Libert (2005). The theories of ordinal and cardinal numbers are developed axiomatically using relevant logic in Weber 2010b, 2012. The possibility of adding a consistency operator to track non-paradoxical fragments of the theory is considered in Omori 2015, taking a cue from the tradition of da Costa. Naive set theory using adaptive logic is presented by Verdée (2013); see Batens 2020 for current developments in adaptive Fregean Set Theory.