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'fragments/reports', 'Foundations without Foundationalism' and 'A Specimen of Discoveries'
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7 ideas
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
13644
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Semantics for models uses set-theory [Shapiro]
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5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
13636
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An axiomatization is 'categorical' if its models are isomorphic, so there is really only one interpretation [Shapiro]
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13670
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Categoricity can't be reached in a first-order language [Shapiro]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13648
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The Löwenheim-Skolem theorems show an explosion of infinite models, so 1st-order is useless for infinity [Shapiro]
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13675
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Substitutional semantics only has countably many terms, so Upward Löwenheim-Skolem trivially fails [Shapiro]
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13659
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Upward Löwenheim-Skolem: each infinite model has infinite models of all sizes [Shapiro]
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13658
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Downward Löwenheim-Skolem: each satisfiable countable set always has countable models [Shapiro]
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