Timeline for The concept of duality
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 31, 2011 at 2:14 | comment | added | Alex | Proofs add more formulas to these sets... like closure operators I guess. The notions of soundness and (in)completeness in logic are probably more interesting than just Galois connetions. | |
| Aug 29, 2011 at 11:15 | comment | added | Emil Jeřábek | What you appear to describe in the first sentence is just the Galois connection between classes of models and sets of formulas. What do proofs have to do with it? | |
| Aug 26, 2011 at 21:38 | comment | added | Alex | The duality is simple: each new axiom or proof technique specifies a subset of true statements, and each model or (counter)example specifies a superset over true statements, i.e. all statements that are true for this model/example. When a bunch of proof techniques and a bunch of models are such that the subset = the superset, you have complete duality. BTW, to those big in categories: do they have a notion of probability? For example imagine a category of extendable computer programs whose meaning is never finally instantiated, and a notion of complexity for them. Just curious... | |
| Aug 26, 2011 at 16:20 | comment | added | Suvrit | Yes, this sounds quite interesting. Please expand if you have a few moments. Thanks. | |
| Aug 26, 2011 at 13:32 | comment | added | Cam McLeman | @Alex: This sounds like a nice entry -- could you elaborate? | |
| Aug 26, 2011 at 9:45 | comment | added | Peter Arndt | How about it? It's a great duality, e.g. its incarnation as Gabriel-Ulmer duality, see ncatlab.org/nlab/show/Gabriel-Ulmer+duality | |
| Aug 26, 2011 at 4:05 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Aug 26, 2011 at 2:13 | history | answered | Alex | CC BY-SA 3.0 |