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Positive abstraction and extensionality
Journal of Symbolic Logic 68 (3):828-836 (2003)
Abstract
It is proved in this paper that the positive abstraction scheme is consistent with extensionality only if one drops equality out of the language. The theory obtained is then compared with GPK, a wellknown set theory based on an extended positive comprehension schemeLinks
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Citations of this work
Logical Consequence and the Paradoxes.Edwin Mares & Francesco Paoli - 2014 - Journal of Philosophical Logic 43 (2-3):439-469.
Assertion, denial and non-classical theories.Greg Restall - 2013 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 81--99.
Theories of truth and the maxim of minimal mutilation.Ole Thomassen Hjortland - 2017 - Synthese 199 (Suppl 3):787-818.
Noncontractive Classical Logic.Lucas Rosenblatt - 2019 - Notre Dame Journal of Formal Logic 60 (4):559-585.
References found in this work
The consistency of the axioms of abstraction and extensionality in a three-valued logic.Ross T. Brady - 1971 - Notre Dame Journal of Formal Logic 12 (4):447-453.
Studies on the axiom of comprehension.Th Skolem - 1963 - Notre Dame Journal of Formal Logic 4 (3):162-170.
Naive Set Theory with Extensionality in Partial Logic and in Paradoxical Logic.Roland Hinnion - 1994 - Notre Dame Journal of Formal Logic 35 (1):15-40.
Investigations on a comprehension axiom without negation in the defining propositional functions.Thoralf Skolem - 1960 - Notre Dame Journal of Formal Logic 1 (1-2):13-22.
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