Psychology 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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David Hilbert on Loewenheim - Dictionary of Arguments
Berka I 340 Loewenheim/Hilbert/Ackermann: Loewenheim has shown that every expression that is universal for the countable domain has the same property for every other domain. In Loewenheim, however, the sentence appears in the dual version: Every formula of the function calculus is either contradictory or can be satisfied within a countable infinite range of thought. >Satisfaction, >Satisfiability, >Models, >Model theory, >Functional calculus, >Countability. General Validity/Hilbert/Ackermann: examples of formulas which are valid in each domain are all formulas that can be proved from axioms of a system. >Validity, >Universal validity. Loewenheim/Hilbert/Ackermann: Loewenheim has made another remarkable proposition: in the treatment of the logical formulas one can restrict oneself to those in which only function symbols with a maximum of two vacancies occur(1). This corresponds to: Schroeder: the general relative calculus can be traced back to the binary calculus(2). >Logical formulas. 1. L. Löwenheim: Über Möglichkeiten im Relativkalkül, Math. Annalen 76 (1915), pp. 447-470, p. 459. 2. D. Hilbert & W. Ackermann: Grundzüge der Theoretischen Logik, Berlin, 6. Aufl. Berlin/Göttingen/Heidelberg 1972, § 12._____________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. |
Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
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> Counter arguments against Hilbert
> Counter arguments in relation to Loewenheim
