Semantics for Naive Set Theory in Many-Valued Logics

Libert, Thierry

doi:10.1007/978-1-4020-5012-7_9

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“…The use of fixed-point theorems in connection with semantics for naive set theory in many-valued logics is detailed in[25].…”

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confidence: 99%

Models for a paraconsistent set theory

Libert

2005

Journal of Applied Logic

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In this paper the existence of natural models for a paraconsistent version of naive set theory is discussed. These stand apart from the previous attempts due to the presence of some non-monotonic ingredients in the comprehension scheme they fulfill. Particularly, it is proved here that allowing the equality relation in formulae defining sets, within an extensional universe, compels the use of nonmonotonic operators. By reviewing the preceding attempts, we show how our models can naturally be obtained as fixed points of some functor acting on a suitable category (stressing the use of fixed-point arguments in obtaining such alternative semantics).

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“…The use of fixed-point theorems in connection with semantics for naive set theory in many-valued logics is detailed in[25].…”

mentioning

confidence: 99%