Economics Dictionary of ArgumentsHome
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| Leopold Löwenheim: Leopold Löwenheim (1878-1957) was a German mathematician who worked on mathematical logic. He is best known for the Löwenheim-Skolem theorem, which states that every first-order theory with an infinite model also has a countable model. See also Models, Model theory, Satisfaction, Satisfiability, Infinity, Countability, Real numbers, Numbers, Word meaning, Reference, Ambiguity._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. | |||
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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. >Real numbers, >Satisfaction, >Models, >Model theory._____________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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