18 ideas
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
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] |
10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
5655 | Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton] |