@article {D:afs, title = {Adaptive Fregean Set Theory}, journal = {Studia Logica}, volume = {108}, year = {2020}, note = {Published online: 10 November 2019}, pages = {903{\textendash}939 (e-published 10 NOV 2019)}, abstract = {

This paper defines provably non-trivial theories that characterize Frege{\textquoteright}s notion of a set, taking into account that the notion is inconsistent. By choosing an adaptive underlying logic, consistent sets behave classically notwithstanding the presence of inconsistent sets. Some of the theories have a full-blown presumably consistent set theory T as a subtheory, provided T is indeed consistent. An unexpected feature is the presence of classical negation within the language.

}, doi = {https://doi.org/10.1007/s11225-019-09882-1}, author = {Batens, Diderik} }