13 ideas
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
17833 | The first-order ZF axiomatisation is highly non-categorical [Hallett,M] |
17834 | Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M] |
17837 | Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M] |
10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
10481 | Models in model theory are structures, not sets of descriptions [Hodges,W] |
17836 | The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M] |
10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
5655 | Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton] |