Combining Texts
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'Model Theory', 'On What Grounds What' and 'Frege on Knowing the Foundations'
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7 ideas
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10478
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Since first-order languages are complete, |= and |- have the same meaning [Hodges,W]
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5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
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|= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]
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5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
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|= should be read as 'is a model for' or 'satisfies' [Hodges,W]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
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A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
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Models in model theory are structures, not sets of descriptions [Hodges,W]
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
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We come to believe mathematical propositions via their grounding in the structure [Burge]
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