本文選題：直覺主義集合論　切入點(diǎn)：策梅洛-弗蘭克爾　出處：《學(xué)術(shù)交流》2017年08期 　論文類型：期刊論文

【摘要】：直覺主義集合論建立在直覺主義而不是經(jīng)典邏輯之上,因此表現(xiàn)了一種基于直覺主義邏輯的、在其中編碼和研究數(shù)學(xué)的自然環(huán)境。作為直覺主義集合論中的典型代表,直覺主義策梅洛-弗蘭克爾集合論是建立在直覺主義邏輯上的策梅洛-弗蘭克爾形式的公理化集合論,它基于僅以二元謂詞符號"屬于"作為其非邏輯符號的一階語言,在帶等詞加上二元謂詞符號"屬于"的直覺主義一階邏輯基礎(chǔ)上公式化。因?yàn)閷τ谥庇X主義邏輯的承諾和對經(jīng)典傳統(tǒng)的背離,直覺主義集合論在集合論的性質(zhì)、公理準(zhǔn)則的選取和公理系統(tǒng)的建構(gòu)上有其獨(dú)特性。而為了更加深入精確地研究直覺主義集合論,需要用到大量的證明論和語義學(xué)技術(shù)。
[Abstract]:Intuitionistic collectivism is based on intuitionism rather than classical logic, so it represents a natural environment in which the code and study of mathematics is based on intuitionistic logic. The intuitionist Zimelo-Frankel set theory is an axiomatic set theory based on the intuitionistic logic. It is based on the first order language which only takes the binary predicate sign "belong" as its non-logical symbol. Formulations are formulated on the basis of the first-order logic of intuitionism, which includes words such as "belong", because of the nature of intuitionistic collectivism in its commitment to the logic of intuitionism and its deviation from classical tradition, The selection of axioms and the construction of axioms have their own uniqueness, but in order to study intuitionism collection theory more accurately, a large number of proofs and semantics techniques are needed.
【作者單位】： 南開大學(xué)哲學(xué)院;
【分類號】：B815.9

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本文編號：1642022