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Christian Thiel on Loewenheim - Dictionary of Arguments

I 321
For example, the paradox of Loewenheim-Skolem: The fact, which can be proven by all axiom systems formulated in classical quantifier logic (with identity), that they can be fulfilled, if at all, then already in a countable individual realm, is quite rightly inferred from this,
I 322
that therefore also such an axiom system for the real numbers must already be countably fulfillable, contrary to the underlying intention to characterize just the not countable totality of the real numbers.


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Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

T I
Chr. Thiel
Philosophie und Mathematik Darmstadt 1995


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Ed. Martin Schulz, access date 2022-09-25
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