16 ideas
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
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] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
10481 | Models in model theory are structures, not sets of descriptions [Hodges,W] |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
10269 | Mathematics eliminates possibility, as being simultaneous actuality in sets [Putnam] |