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Ideas of Wilfrid Hodges, by Text
[British, b.1941, Of Bedford College, then Queen Mary and Westfield, London.]
1.1

p.9

10282

Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former)

1.10

p.29

10288

Down LöwenheimSkolem: if a countable language has a consistent theory, that has a countable model

1.10

p.29

10289

Up LöwenheimSkolem: if infinite models, then arbitrarily large models

1.10

p.29

10287

If a firstorder theory entails a sentence, there is a finite subset of the theory which entails it

1.3

p.13

10283

A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables

1.3

p.13

10284

There are three different standard presentations of semantics

1.5

p.17

10285

I = φ means that the formula φ is true in the interpretation I

1.6

p.19

10286

A 'set' is a mathematically wellbehaved class

Intro

p.1

10473

Model theory studies formal or natural languageinterpretation using settheory

1

p.1

10474

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

1

p.2

10475

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

2

p.7

10476

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

3

p.7

10477

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

3

p.8

10478

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

4

p.11

10480

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

5

p.12

10481

Models in model theory are structures, not sets of descriptions
