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Path: ...!weretis.net!feeder8.news.weretis.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Mikko <mikko.levanto@iki.fi> Newsgroups: sci.logic Subject: Re: This makes all Analytic(Olcott) truth computable --- ZFC Date: Thu, 22 Aug 2024 15:21:51 +0300 Organization: - Lines: 53 Message-ID: <va7agv$eab6$1@dont-email.me> References: <v86olp$5km4$1@dont-email.me> <v95c2j$p5rb$4@dont-email.me> <v95cke$p5rb$5@dont-email.me> <v977fo$gsru$1@dont-email.me> <v97goj$ielu$1@dont-email.me> <v9c93e$35sg6$1@dont-email.me> <v9d3k1$3ajip$1@dont-email.me> <v9ffpr$3s45o$1@dont-email.me> <v9fkd4$3se8c$1@dont-email.me> <v9kg66$tdvb$1@dont-email.me> <v9nbjf$1dj8q$1@dont-email.me> <20b1dea98eda49e74e822c96b37565bb3eb36013@i2pn2.org> <v9o4p2$1h5u4$1@dont-email.me> <cd12fb81fcd05d2e112fc8aca2f5b791c521cfc9@i2pn2.org> <v9oddf$1i745$2@dont-email.me> <7f2a1f77084810d4cee18ac3b44251601380b93a@i2pn2.org> <v9ogmp$1i745$6@dont-email.me> <662de0ccc3dc5a5f0be0918d340aa3314d51a348@i2pn2.org> <v9oj4r$1i745$8@dont-email.me> <v9sibq$2bq1o$1@dont-email.me> <v9sn85$2c67u$6@dont-email.me> <v9v0u0$2qajg$1@dont-email.me> <v9vgbu$2rjt1$13@dont-email.me> <va1qmi$3biht$1@dont-email.me> <va27ge$3cvgv$7@dont-email.me> <va4a0u$3q89u$1@dont-email.me> <va4n2u$3s0hu$3@dont-email.me> <MPG.413129831ae549849896ff@reader.eternal-september.org> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 22 Aug 2024 14:21:52 +0200 (CEST) Injection-Info: dont-email.me; posting-host="b61e73617b836bb657aca38e501dcccb"; logging-data="469350"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18BTP4tJP6VLQoWHdWfSLPY" User-Agent: Unison/2.2 Cancel-Lock: sha1:iDTmI8p11UwyF9BDG9UaDHH4t8Q= Bytes: 3858 On 2024-08-22 09:55:51 +0000, Wasell said: > On Wed, 21 Aug 2024 07:37:50 -0500, in article <va4n2u$3s0hu$3@dont-email.me>, > olcott wrote: >> On 8/21/2024 3:54 AM, Mikko wrote: >>> On 2024-08-20 13:59:42 +0000, olcott said: >>> >>>> On 8/20/2024 5:21 AM, Mikko wrote: > > [...] > >>>>> Set theories with an unversal set need to restrict >>>>> the construction operations more than what is usually considered >>>>> reasonable. >>>> >>>> I don't see how. The set of all sets that do not contain >>>> themselves simply becomes the set of all sets. >>> >>> The set of all sets that do not contain themselves is the Russell set >>> that revealied the inconsistency of the naive set theory. The main >>> improvment in ZF was the non-existence of this set. >> >> So basically you agreed with me on everything. > > Oh, you blithering imbecile! The universal set V is, by definition, Often U is used instead of V for the universal set. V is often the smallest set that conains the empty set and every set that can be constructed from other members of V. > an element of itself. It is a set, and therefore an element of the > set of all sets. > > By Specification, we can split V into the set of all sets that have > themselves as an element, and its complement, the set of all sets > that are not elements of themselves. Neither of these two sets are > empty. > > Do you see where this is going? Or do you need more hand holding? > > There are set theories with a universal set, but they also > have restricted Specification. (Or, more commonly, no Axiom of > Specification, but a restricted Comprehension instead.) If every set has a power set then the univesal has a power set, too, and the power set of the universal set is a member of the univerasl set. One must be careful with axioms or one can prove someting false from the exstence of a set that has its poverset (and the power set of its powerset) as a member. -- Mikko