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 ,]].
Click on the Idea Number for the full details 
back to texts

expand these ideas
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. FirstOrder Logic
10478

Since firstorder languages are complete, = and  have the same meaning

5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence =
10477

= in modeltheory means 'logical consequence'  it holds in all models

5. Theory of Logic / I. Semantics of Logic / 5. Satisfaction
10474

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

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10473

Model theory studies formal or natural languageinterpretation using settheory

10481

Models in model theory are structures, not sets of descriptions

10475

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

6. Mathematics / A. Nature of Mathematics / 4. The Infinite / i. Cardinal infinity
10480

Firstorder logic can't discriminate between one infinite cardinal and another
