Caros colegas: Em vista do interesse do assunto, julgamos apropriado divulgar, abraços, Walter ========================= Twist-Valued Models for Three-valued Paraconsistent Set Theory W. Carnielli and M. E. Coniglio https://arxiv.org/pdf/1911.11833.pdf
Light abstract: Paraconsistent set theory (PST) is the theoretical move to maintain the freedom of defining sets, while stripping the theory of unnecessary principles, so as to avoid triviality -- a disastrous consequences of contradictions involving sets in ZF. A hard problem is to find good models for PST. B. Löwe and S. Tarafder proposed in 2015 a class of algebras based on a certain kind of implication which satisfy several axioms of ZF. From this class, they found a specific 3-valued model called PS3 which satisfies all the axioms of ZF, and can be expanded with a paraconsistent negation *, thus obtaining a paraconsistent model of ZF. The logic (PS3 ,*) coincides (up to the language) with da Costa and D'Ottaviano logic J3, a 3-valued paraconsistent logic that have been proposed independently in the literature by several authors and with different motivations such as CluNs, LFI1 and MPT. We propose in this paper a family of algebraic models of ZFC based on LPT0, another linguistic variant of J3 introduced by us in 2016. The semantics of LPT0, as well as of its first-order version QLPT0, is given by twist structures defined over Boolean algebras. Twist-valued models are natural generalizations of the Boolean-valued models of set theory independently introduced by Scott, Solovay and Vopěnka. Our twist-valued models are adapted to provide a class of twist-valued models for (PS3,*), thus generalizing Löwe and Tarafder's results. It is shown that they are in fact models of ZFC (not only of ZF). ==================================== Walter Carnielli https://waltercarnielli.com/ Centre for Logic, Epistemology and the History of Science and Department of Philosophy State University of Campinas –UNICAMP 13083-859 Campinas -SP, Brazil CV Lattes : http://lattes.cnpq.br/1055555496835379 -- Você está recebendo esta mensagem porque se inscreveu no grupo "LOGICA-L" dos Grupos do Google. Para cancelar inscrição nesse grupo e parar de receber e-mails dele, envie um e-mail para [email protected]. Para ver esta discussão na web, acesse https://groups.google.com/a/dimap.ufrn.br/d/msgid/logica-l/CA%2Bob58PmnD0nmGai5Fz4kfeJ_Dd%3DTq0Z%3DnVeFH9Y22F1GdeMeQ%40mail.gmail.com.
