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- W2118397869 abstract "If a contradiction is deduced by using only the defining formula of a set, it is called a contradiction of Russell's type , and the set is called inconsistent . A set is called consistent , if no contradiction can be deduced from the defining formula of the set. The object of this note is to determine some conditions for some sets to be consistent or inconsistent. In §1 notations and terms are defined. In §2 main results are stated. In §3, the proof in UL of a contradiction is simplified for a special kind of sets, so that a simplified definition of the proof of a contradiction is given for the kind of sets, and some properties of a proof in UL are stated concerning the simplified definition. This definition and the properties of a proof are the basis of the proof of the results given in §§5–10. Thus, this Part (V), except §3, is written independently of other Parts as far as possible. However, it depends essentially on Parts (I) and (II). In §4 some examples are given." @default.
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- W2118397869 date "1958-12-01" @default.
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- W2118397869 title "An investigation on the logical structure of mathematics (V). Contradictions of Russell's type " @default.
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- W2118397869 doi "https://doi.org/10.2307/2964014" @default.
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