Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Fri, 31 Jan 2025 11:21:58 +0100
Organization: A noiseless patient Spider
Lines: 17
Message-ID: <vni886$3f2gg$2@dont-email.me>
References: <vmo1bs$1rnl$1@dont-email.me>
 <27377646-137a-4f8f-a7bb-a75707b2da96@att.net> <vn2gcf$2ouuo$2@dont-email.me>
 <965ee9868f28953d437113d0d38f069815499a3f@i2pn2.org>
 <vn4sfi$3ijdb$2@dont-email.me>
 <e51fcde5622ccc6beab7882831e5f7033c04d150@i2pn2.org>
 <vn5gur$3qu1c$3@dont-email.me>
 <77fb6230f3ef78f7524b70785c4772313e238258@i2pn2.org>
 <vn7r2r$q7sl$2@dont-email.me>
 <814297ada299a65bb9f427ddec5646afcc94be9f@i2pn2.org>
 <vn85es$u7pk$2@dont-email.me>
 <f753327bd316219fc9f04a8626b725956bfe8c9a@i2pn2.org>
 <vna675$1ng1j$1@dont-email.me>
 <b9a5e6e3397b079bfb37f810d53d3491a400b3d6@i2pn2.org>
 <vnasam$1s6ha$3@dont-email.me>
 <95ac176b19f1c24772a2ee73b3a12fe494da1241@i2pn2.org>
 <vncqhg$29v5v$3@dont-email.me> <vncsrh$2anj5$1@dont-email.me>
 <993b552f-7ab8-4a0b-a308-4748f20efb95@tha.de> <vndcal$2dft2$1@dont-email.me>
 <vnffdk$2rv3s$3@dont-email.me>
 <9e3c198cdfa1b264a1e30723ff18538f02e59af0@i2pn2.org>
 <vngjss$31ubc$1@dont-email.me>
 <d89c793e1e0a14f531ef1699066785dfd6b4b98b@i2pn2.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Fri, 31 Jan 2025 11:21:58 +0100 (CET)
Injection-Info: dont-email.me; posting-host="e88c9309437777936f7e1b85394b096b";
	logging-data="3639824"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+VkzmFMTT3QwzT3RE17mMbJ8TL4q4AoUM="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:kd2ZLz/tbq+qKmwf55q8KiykZ9g=
In-Reply-To: <d89c793e1e0a14f531ef1699066785dfd6b4b98b@i2pn2.org>
Content-Language: en-US
Bytes: 2548

On 31.01.2025 02:02, Richard Damon wrote:
> On 1/30/25 2:28 PM, WM wrote:

>> But a set that has union ℕ is a set.
> 
> But since the "Set of Necessary FISONs" isn't actually a "Set"

take the set O of v. Neumann ordinals A(n) that you claim satisfies 
U(A(n)) = ℕ.

 From this set O every finite subset can be subtracted without changing 
the result. Therefore,  by induction, no finite A(n) remains. Therefore 
the set O has no first ordinal. Therefore it is not a set of ordinals. 
Therefore your claim is wrong.

Regards, WM