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Ideas of Wilfrid Hodges, by Text
[British, b.1941, Of Bedford College, then Queen Mary and Westfield, London.]
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1.1
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p.9
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10282
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Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former)
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1.10
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p.29
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10287
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If a first-order theory entails a sentence, there is a finite subset of the theory which entails it
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1.10
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p.29
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10289
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Up Löwenheim-Skolem: if infinite models, then arbitrarily large models
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1.10
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p.29
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10288
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Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model
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1.3
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p.13
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10283
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A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables
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1.3
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p.13
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10284
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There are three different standard presentations of semantics
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1.5
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p.17
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10285
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I |= φ means that the formula φ is true in the interpretation I
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1.6
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p.19
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10286
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A 'set' is a mathematically well-behaved class
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Intro
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p.1
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10473
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Model theory studies formal or natural language-interpretation using set-theory
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1
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p.1
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10474
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|= should be read as 'is a model for' or 'satisfies'
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1
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p.2
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10475
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A 'structure' is an interpretation specifying objects and classes of quantification
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2
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p.7
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10476
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The idea that groups of concepts could be 'implicitly defined' was abandoned
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3
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p.7
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10477
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|= in model-theory means 'logical consequence' - it holds in all models
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3
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p.8
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10478
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Since first-order languages are complete, |= and |- have the same meaning
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4
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p.11
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10480
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First-order logic can't discriminate between one infinite cardinal and another
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5
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p.12
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10481
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Models in model theory are structures, not sets of descriptions
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