The consistency of the axioms of abstraction and extensionality in a three-valued logic.
Ross T. Brady · Notre Dame Journal of Formal Logic · 1971
The Abstraction Axiom I want to consider is the following one, which is based on the Lukasiewicz three-valued logic.1. To construct the model, we need to extend the wffs used above to express (*) by adding some terms, some of which will be used as the domain of the model.We give the formation rules for terms and wffs as follows:1.If x and y are set variables, then xεy is an atomic wff. Any combination of wffs using ~, ->, A are wffs.3. A propositional constant (i.e., 1, \ or 0) is an atomic wff.