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

10476

The idea that groups of concepts could be 'implicitly defined' was abandoned

5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic

10478

Since first-order languages are complete, |= and |- have the same meaning

5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=

10477

|= in model-theory means 'logical consequence' - it holds in all models

5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction

10474

|= should be read as 'is a model for' or 'satisfies'

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models

10475

A 'structure' is an interpretation specifying objects and classes of quantification

10473

Model theory studies formal or natural language-interpretation using set-theory

10481

Models in model theory are structures, not sets of descriptions

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

10480

First-order logic can't discriminate between one infinite cardinal and another