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Ideas for 'Stipulation, Meaning and Apriority', 'Cantorian Abstraction: Recon. and Defence' and 'First-Order Logic'

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2 ideas

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

10288	Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W]
	Full Idea: Downward Löwenheim-Skolem (the weakest form): If L is a first-order language with at most countably many formulas, and T is a consistent theory in L. Then T has a model with at most countably many elements.
	From: Wilfrid Hodges (First-Order Logic [2001], 1.10)

10289	Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
	Full Idea: Upward Löwenheim-Skolem: every first-order theory with infinite models has arbitrarily large models.
	From: Wilfrid Hodges (First-Order Logic [2001], 1.10)