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Leopold Löwenheim [ˈle:o:pɔl̩d ˈlø:vɛnhaɪm] (26 June 1878 in
Krefeld – 5 May 1957 in Berlin) was a
German mathematician doing work in
mathematical logic...
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mathematical logic, the
Löwenheim–Skolem
theorem is a
theorem on the
existence and
cardinality of models,
named after Leopold Löwenheim and
Thoralf Skolem...
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could contain an
uncountable set. The
paradox arises from part of the
Löwenheim–Skolem theorem;
Thoralf Skolem was the
first to
discuss the seemingly...
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mathematical logic the
Löwenheim number of an
abstract logic is the
smallest cardinal number for
which a weak
downward Löwenheim–Skolem
theorem holds....
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theorems that make it
amenable to
analysis in
proof theory, such as the
Löwenheim–Skolem
theorem and the
compactness theorem. First-order
logic is the standard...
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greatly simplified the
proof of a
theorem Leopold Löwenheim first proved in 1915,
resulting in the
Löwenheim–Skolem theorem,
which states that if a countable...
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Another cornerstone of first-order
model theory is the
Löwenheim-Skolem theorem.
According to the
Löwenheim-Skolem Theorem,
every infinite structure in a countable...
- over to second-order
logic with
Henkin semantics.
Since also the Skolem–
Löwenheim theorems hold for
Henkin semantics, Lindström's
theorem imports that Henkin...
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compactness theorem is one of the two key properties,
along with the
downward Löwenheim–Skolem theorem, that is used in Lindström's
theorem to
characterize first-order...
- {\displaystyle \Rightarrow }
Löwenheim–Skolem theorem" — that is, D C {\displaystyle {\mathsf {DC}}}
implies the
Löwenheim–Skolem theorem. See
table Moore...
