Timeline for Elementary extensions and type spaces
Current License: CC BY-SA 3.0
4 events
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| May 12, 2013 at 13:50 | comment | added | KristianJS | I would say in that example that you know something very interesting about the relationship between M and N actually. However, I appreciate the point that type spaces are perhaps quite bad at telling structures apart. Perhaps in certain specific cases though you can say something. I'll leave this question open for now. | |
| May 12, 2013 at 6:07 | comment | added | Pierre Simon | If I understand well, you want to look at type spaces as pure topological spaces and ask if maps between them translate to maps between the structures. This is hopeless, because the topological structure of type space does not carry enough information. For an easy counter-example, take the ring language. M is an ordinary ring and N is the same as M, but exchanging the roles of addition and multiplication. The type spaces are homeomorphic, but clearly the structures are completely different. | |
| May 11, 2013 at 22:11 | comment | added | KristianJS | Thanks for pointing this out. However, it does not answer the question. I have edited it to be more general to take into account non-trivial maps as well. | |
| May 11, 2013 at 19:46 | history | answered | Pierre Simon | CC BY-SA 3.0 |