Timeline for Notion of internality in model theory
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 6, 2011 at 3:52 | answer | added | Dave Marker | timeline score: 9 | |
| Dec 6, 2011 at 2:17 | answer | added | John Baldwin | timeline score: 4 | |
| Dec 5, 2011 at 19:12 | answer | added | none | timeline score: 0 | |
| Dec 1, 2011 at 17:26 | comment | added | Noah Schweber | Internality can also show up if you're dealing with a model of a theory which can define notions like "finite," "well-ordered," etc. So, for example, we can have a model $M$ of ZFC set theory and some $x\in M$ such that $M\models$ "$x$ is finite," and yet still have infinitely many $y\in M$ with $M\models y\in x$; this would be an example of an infinite internally finite object. In nonstandard analysis, there is a similar distinction between internal sets, which are sets that a given model "sees," and sets in general. Is this what you're interested in? | |
| Dec 1, 2011 at 16:54 | comment | added | Ed Dean | I'm entirely guessing what you're after of course, but are you perhaps thinking of inner model theory? en.wikipedia.org/wiki/Inner_model_theory | |
| Dec 1, 2011 at 10:50 | comment | added | user19660 | Thank you Buschi for your help but David Roberts is right en.wikipedia.org/wiki/Model_theory is what I meant. @David Roberts Thank you for your answer. I heard this term in a seminar. I can't give specific reference but I'm a beginner. | |
| Nov 30, 2011 at 21:29 | comment | added | David Roberts♦ | @Buschi - I disagree. There is 'model theory' which has no connections to category theory whatsoever: en.wikipedia.org/wiki/Model_theory @Alphonse - is this what you meant? And please provide a reference as to where you heard about internality. People need to know at what level to pitch their answers. | |
| Nov 30, 2011 at 16:44 | comment | added | Buschi Sergio | I'm no in logic too muchm, but I guess that you have to know the internal logic in some categories/topos, see the P. Johnstone book o on topos theory | |
| Nov 30, 2011 at 16:40 | history | asked | Alphonse Dalbin | CC BY-SA 3.0 |