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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: immibis <news@immibis.com> Newsgroups: comp.theory Subject: Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets Date: Sat, 1 Jun 2024 23:36:31 +0200 Organization: A noiseless patient Spider Lines: 20 Message-ID: <v3g48v$2vmuc$2@dont-email.me> References: <v3501h$lpnh$1@dont-email.me> <v3ci7v$283tt$1@dont-email.me> <v3cr8n$29gdk$2@dont-email.me> <v3eljo$2migl$1@dont-email.me> <v3fck6$2qsgd$3@dont-email.me> <v3fqt9$2o13h$8@i2pn2.org> <v3fubs$2ulbk$2@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 01 Jun 2024 23:36:31 +0200 (CEST) Injection-Info: dont-email.me; posting-host="d7768fc7c60e5dabfd7a19d675cbc7e5"; logging-data="3136460"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/SjtS+5H6OMWkXs+DfXYs0" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:ed7EvRwI0l3ya/eZB1p+VlAu5BE= In-Reply-To: <v3fubs$2ulbk$2@dont-email.me> Content-Language: en-US Bytes: 1874 On 1/06/24 21:55, olcott wrote: > On 6/1/2024 1:56 PM, joes wrote: >> I misunderstood this, too, but we want a single machine that solves the >> problem on its own, not multiple that each solve parts. There could be >> many such machines. >> > > ∃H ∈ Turing_Machines > is fulfilled when there are one or more machines that independently > solve the halting problem. > > ∃!H ∈ Turing_Machines > is ONLY fulfilled when there is exactly one machine that solves the > halting problem. > > I knew what Linz meant from all the other proofs that I read. > > This is a rare instance of Olcott being correct.