The sentence "contains all the info about any model" is ambiguous. I mean the theory contains everything you can say that is correct about every model. --C On Sun, May 27, 2012 at 9:02 AM, Charles Wells <charles@abstractmath.org>wrote:
Data and conditions constitute a presentation. The graph, diagrams, cones & cocones of a sketch are a presentation. This idea has not been superseded, not at all, but it has been completed (in two senses) by the concept of theory, which is the object generated by the presentation: The theory of a sketch, the classifiying topos, the algebraic theory in the sense of Lawvere, and so on. This object contains all the information about any model.
That idea is in some way the other face of, or the complementary point of view about, data and conditions.
Charles
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