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'fragments/reports', 'Introduction to the Philosophy of Mathematics' and 'Higher-Order Logic'
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5 ideas
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10590
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Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
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10296
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The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
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10297
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The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
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10292
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Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
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17929
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Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan]
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