2001 | First-Order Logic |
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 | 10289 | Up Löwenheim-Skolem: if infinite models, then arbitrarily large models |
1.10 | p.29 | 10288 | Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model |
1.10 | p.29 | 10287 | If a first-order 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 well-behaved class |
2005 | Model Theory |
Intro | p.1 | 10473 | Model theory studies formal or natural language-interpretation using set-theory |
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 model-theory means 'logical consequence' - it holds in all models |
3 | p.8 | 10478 | Since first-order languages are complete, |= and |- have the same meaning |
4 | p.11 | 10480 | First-order logic can't discriminate between one infinite cardinal and another |
5 | p.12 | 10481 | Models in model theory are structures, not sets of descriptions |