We presume a background theory which allows for indeterminacy of states of affairs involving objects, extending even to indeterminacy of identity between objects. A sentence reporting such an indeterminate state of affairs lacks truth-value. We extend this to a theory of sets, similar to ZFU, in which membership in, and identity between, sets may also be indeterminate.
"Set Theory with Indeterminacy of Identity." Notre Dame J. Formal Logic 40 (4) 473 - 495, Fall 1999. https://doi.org/10.1305/ndjfl/1012429714