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Ideas of Wilfrid Hodges, by Text

[British, b.1941, Of Bedford College, then Queen Mary and Westfield, London.]

2001 First-Order Logic
1.1 p.9 Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former)
1.10 p.29 Down L÷wenheim-Skolem: if a countable language has a consistent theory, that has a countable model
1.10 p.29 Up L÷wenheim-Skolem: if infinite models, then arbitrarily large models
1.10 p.29 If a first-order theory entails a sentence, there is a finite subset of the theory which entails it
1.3 p.13 A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables
1.3 p.13 There are three different standard presentations of semantics
1.5 p.17 I |= φ means that the formula φ is true in the interpretation I
1.6 p.19 A 'set' is a mathematically well-behaved class
2005 Model Theory
Intro p.1 Model theory studies formal or natural language-interpretation using set-theory
1 p.1 |= should be read as 'is a model for' or 'satisfies'
1 p.2 A 'structure' is an interpretation specifying objects and classes of quantification
2 p.7 The idea that groups of concepts could be 'implicitly defined' was abandoned
3 p.7 |= in model-theory means 'logical consequence' - it holds in all models
3 p.8 Since first-order languages are complete, |= and |- have the same meaning
4 p.11 First-order logic can't discriminate between one infinite cardinal and another
5 p.12 Models in model theory are structures, not sets of descriptions