论集合论的模型  

On the Models of Set Theory

作　　者：李娜[1] 何建锋 Na Li;Jianfeng He(School of Philosophy,Nankai University)

机构地区：[1]南开大学哲学院

出　　处：《逻辑学研究》2019年第1期49-69,共21页Studies in Logic

基　　金：国家社科基金重点项目"基于哲学逻辑的集合论研究"(16AZD036)

摘　　要：本文讨论了ZF的经典模型和非经典模型,梳理了它们的最新动态,并且将ZF的广义代数值模型推广到基于形式不一致逻辑的弗协调集合论。该推广过程的关键在于解决两个问题:第一,这类弗协调集合论是否包含不是一致的集合;第二,在模型中如何处理相等关系=,以便它能够满足莱布尼兹公理。此外,本文构造的广义代数值模型具有一定的可推广性。In this paper,the classical and non-classical models of ZF are discussed,their latest developments are summarized,and the generalized algebra-valued model of ZF is generalized to the paraconsistent set theories based on the logics of formal inconsistency.The key of this generalization process is to solve two problems:first,whether this kind of paraconsistent set theory contains inconsistent sets;second,how to deal with equality relation=in the model so that it can satisfy Leibniz axiom.In addition,the generalized algebra-valued model constructed in this paper has certain generalizability.

关 键 词：集合论的模型 独立性 布尔值 拓扑斯 弗协调集合论 

分 类 号：B81[哲学宗教—逻辑学]