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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: The reality of sets, on a scale of 1 to 10 [Was: The
 non-existence of "dark numbers"]
Date: Tue, 25 Mar 2025 03:16:12 +0100
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Am 25.03.2025 um 03:10 schrieb Moebius:
> Am 24.03.2025 um 22:44 schrieb Moebius:
> 
>> "Die gesamte Mathematik inklusive der klassischen Zahlenbereiche läßt 
>> sich als Teilgebiet der Mengenlehre auffassen." ["All of mathematics, 
>> including classical number domains, can be regarded as a subfield of 
>> set theory."] (A. Oberschelp, Aufbau des Zahhlensystems, 1968)
> 
> Too polemic?
> 
> How about: "Die meisten Teile der Mathematik inklusive der klassischen 
> Zahlenbereiche lassen sich als Teilgebiet der Mengenlehre 
> auffassen." ["Most parts of mathematics, including classical number 
> domains, can be regarded as a subfield of set theory."]

For example, the "collection" of all groups does not form a set. (!)

But we can deal with such "collections" (proper classes) in "set 
theories" like NBG and/or MK. So the claim of Oberschelp still holds (at 
least for these cases).

>> Lit.: https://en.wikipedia.org/wiki/Arnold_Oberschelp