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Path: ...!Xl.tags.giganews.com!local-3.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Mon, 29 Jul 2024 19:44:50 +0000 Subject: Re: Replacement of Cardinality Newsgroups: sci.logic,sci.math References: <hsRF8g6ZiIZRPFaWbZaL2jR1IiU@jntp> <881fc1a1-2e55-4f13-8beb-94d1f941b5af@att.net> <vg44QVKbPSR4U0Tq71L-fg5yqgM@jntp> <85194aeb-1b24-4486-8bcc-4dcd43b4fd2f@att.net> <HVudnVg62uHETjv7nZ2dnZfqn_ednZ2d@giganews.com> <HVudnVo62uGFSDv7nZ2dnZfqn_ednZ2d@giganews.com> <tR-dnU_G9dTXSjv7nZ2dnZfqn_WdnZ2d@giganews.com> <2e188e21-4128-4c76-ba5d-473528262931@att.net> From: Ross Finlayson <ross.a.finlayson@gmail.com> Date: Mon, 29 Jul 2024 12:44:59 -0700 User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101 Thunderbird/38.6.0 MIME-Version: 1.0 In-Reply-To: <2e188e21-4128-4c76-ba5d-473528262931@att.net> Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 7bit Message-ID: <NQednW9Dop2vbDr7nZ2dnZfqn_SdnZ2d@giganews.com> Lines: 39 X-Usenet-Provider: http://www.giganews.com X-Trace: sv3-0eCrsduOQtxmcn07Nh/Ac8f3QzRBiArOZJqTcypeEmBhbnwmmwfHJDiVU1fOKbJfNgC21CUhuP8WD0z!FkhJlVvLeudqTw4IMqrFP+gRV8zp01gq5bs5iCOxfx+lF/9wgPenr2rdwS5g/nUzmWCXSXg3whgU X-Complaints-To: abuse@giganews.com X-DMCA-Notifications: http://www.giganews.com/info/dmca.html X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.3.40 Bytes: 2738 On 07/29/2024 05:32 AM, Jim Burns wrote: > On 7/28/2024 7:42 PM, Ross Finlayson wrote: >> On 07/28/2024 04:32 PM, Ross Finlayson wrote: >>> On 07/28/2024 04:25 PM, Ross Finlayson wrote: >>>> On 07/28/2024 11:17 AM, Jim Burns wrote: > >>>>> [...] >>>> [...] >>> [...] >> >> about ubiquitous ordinals > > What are ubiquitous ordinal? > > Well, you know that ORD, is, the order type of ordinals, and so it's an ordinal, of all the ordinals. The "ubiquitous ordinals", sort of recalls Kronecker's "G-d made the integers, the rest is the work of Man", that the Integer Continuum, is the model and ground model, of any sort of language of finite words, like set theory. It's like the universe of set theory, then as that there's _always_ an arithmetization, or as with regards to ordering and numbering as a bit weaker property than collecting and counting, so that "ubiquitous ordinals" is what you get from a discrete world. Then there's that according to the set-theoretic Powerset theorem of Cantor, that when the putative function is successor, in ubiquitous ordinals where order type is powerset is successor, then there's no missing element. So, "ubiquitous ordinals" is exactly what it says.