Ideas from 'Model Theory' by Wilfrid Hodges [2005], by Theme Structure

[found in 'Stanford Online Encyclopaedia of Philosophy' (ed/tr Stanford University) [plato.stanford.edu ,-]].

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2. Reason / D. Definition / 7. Contextual Definition
The idea that groups of concepts could be 'implicitly defined' was abandoned
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
Since first-order languages are complete, |= and |- have the same meaning
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
|= in model-theory means 'logical consequence' - it holds in all models
5. Theory of Logic / I. Semantics of Logic / 5. Satisfaction
|= should be read as 'is a model for' or 'satisfies'
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Model theory studies formal or natural language-interpretation using set-theory
Models in model theory are structures, not sets of descriptions
A 'structure' is an interpretation specifying objects and classes of quantification
6. Mathematics / A. Nature of Mathematics / 4. The Infinite / i. Cardinal infinity
First-order logic can't discriminate between one infinite cardinal and another