Pode ser de interesse para alguns dos colegas. JM
------------------------------------------------------------------------------ \\ arXiv:2210.00057 Date: Fri, 30 Sep 2022 19:39:37 GMT (37kb) Title: Paraconsistent and Paracomplete Zermelo-Fraenkel Set Theory Authors: Yurii Khomskii, Hrafn Valt\'yr Oddsson Categories: math.LO MSC-class: 03E70, 03B53, 03B60 \\ We present a novel treatment of set theory in a four-valued paracomplete and paraconsistent logic, i.e., a logic in which propositions can be neither true nor false, and can be both true and false. By prioritising a system with an ontology of non-classical sets that is easy to understand and apply in practice, our approach overcomes many of the obstacles encountered in previous attempts at such a formalization. We propose an axiomatic system BZFC, obtained by analysing the ZFC-axioms and translating them to a four-valued setting in a careful manner. We introduce the anti-classicality axiom postulating the existence of non-classical sets, and prove a surprising results stating that the existence of a single non-classical set is sufficient to produce any other type of non-classical set. We also look at bi-interpretability results between BZFC and classical ZFC, and provide an application concerning Tarski semantics, showing that the classical definition of the satisfaction relation yields a logic precisely reflecting the non-classicality in the meta-theory. \\ ( https://arxiv.org/abs/2210.00057 , 37kb) ------------------------------------------------------------------------------ -- LOGICA-L Lista acadêmica brasileira dos profissionais e estudantes da área de Lógica <logica-l@dimap.ufrn.br> --- 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/CAO6j_Lj6HYAzv6X_b05Zf%2BhiLpiqUhR5C9VZy3Yxia5%2BA_dDuw%40mail.gmail.com.
