more on this theme | more from this thinker
Full Idea
A 'structure' in model theory is an interpretation which explains what objects some expressions refer to, and what classes some quantifiers range over.
Gist of Idea
A 'structure' is an interpretation specifying objects and classes of quantification
Source
Wilfrid Hodges (Model Theory [2005], 1)
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.2
A Reaction
He cites as examples 'first-order structures' used in mathematical model theory, and 'Kripke structures' used in model theory for modal logic. A structure is also called a 'universe'.
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] |
10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
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] |
10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
10481 | Models in model theory are structures, not sets of descriptions [Hodges,W] |