Caro Walter, Já que levantou o assunto, vou fazer uma pergunta:
Os conjuntos paraconsistentes existem? Uma paráfrase possível para essa pergunta: o que garante a existência de conjuntos paraconsistentes? Obrigado Em qui, 5 de dez de 2019 12:36, Walter Carnielli <walter.carnie...@gmail.com> escreveu: > 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 logica-l+unsubscr...@dimap.ufrn.br. > 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 > . > -- 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 logica-l+unsubscr...@dimap.ufrn.br. Para ver esta discussão na web, acesse https://groups.google.com/a/dimap.ufrn.br/d/msgid/logica-l/CAEsiyHSZRUCHivwXM9LuYndKuUekLdobik3aScxad%3DcKi1sptQ%40mail.gmail.com.
