Subjects: Mathematics >> Mathematics （General） Subjects: Mathematics >> Logic submitted time 2023-06-20
Abstract： 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 different methods. Finally, we introduce the residually finite residuated lattices and characterize them from algebraic, logical and topological perspectives,
respectively.
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Subjects: Mathematics >> Logic submitted time 2018-09-28
Abstract： In order to fundamentally eliminate all kinds of paradoxes existing in mathematic foundation and make mathematics architecture on a highly reliable basis, it was found that formal logic can only be used in the discussion domain (called the feasible domain) in which all of the three laws, i,e, the law of identity, the law of non-contradictory and the law of excluded middle are hold true. Otherwise, various errors including public opinion will occur. It was concluded that in feasible domain, as long as the premise is reliable and the derivation is strict, no paradox exists. Some historically famous paradoxes such as liar paradox and barber paradox were therefore analyzed. At the same time, the logical mistakes in the application of Piano axiom, in the proofs of Cantor's theorem, the interval method and diagonal argument were pointed out. Suggestion for a uniform definition of natural numbers, rational numbers and irrational numbers to avoid any errors was therefore proposed. " "
Peer Review Status:Awaiting Review
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