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• W791043903 abstract "It is a commonplace of set theory to say that there is no set of all well-orderings nor a set of all sets. We are implored to accept this due to the threat of paradox and the ensuing descent into unintelligibility. In the absence of promising alternatives, we tend to take up a conservative stance and tow the line: there is no universe (Halmos, in: Naive set theory, 1960). In this paper, I am going to challenge this claim by taking seriously the idea that we can talk about the collection of all the sets and many more collections beyond that. A method of articulating this idea is offered through an indefinitely extending hierarchy of set theories. It is argued that this approach provides a natural extension to ordinary set theory and leaves ordinary mathematical practice untouched." @default.
• W791043903 created "2016-06-24" @default.
• W791043903 creator A5007697398 @default.
• W791043903 date "2015-07-08" @default.
• W791043903 modified "2023-10-16" @default.
• W791043903 title "Sets and supersets" @default.
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• W791043903 doi "https://doi.org/10.1007/s11229-015-0818-x" @default.
• W791043903 hasPublicationYear "2015" @default.
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