分类: 数学 >> 数学(综合) 分类: 数学 >> 逻辑 提交时间: 2023-06-20
摘要: The aim of this paper is to study well-connected residuated lattices and residually finite residuated lattices. So far, well-connected residuated lattices not only a main tool for studying RLsi but also a subdirect irreducible representation object of residuated lattices. In this paper we both investigate the above two aspects by using some di#11;erent methods. Finally, we introduce the residually finite residuated lattices and characterize them from algebraic, logical and topological perspectives, respectively.
摘要: 为了从根本上消灭存在于数学基础中的各种悖论,使数学建筑在高度可靠的基础上,发现形式逻辑只能用于同一律,矛盾律和排中律这三大规律都成立的讨论域 (称为可行域) 内,否则就会产生包括悖论在内的各种错误,而在形式逻辑的适用范围即可行域内,只要前提可靠,推导严格,悖论是不存在的。根据该结论,分析了说谎者悖论和理发师悖论等一些历史上比较著名的悖论的形成原因,同时指出了数学基础中皮亚诺公理的应用和康托尔定理、区间套和对角线法证明中的一些逻辑错误,提出了能够避免这些错误的统一的定义自然数、有理数和无理数的建议。