Timeline for Confusion about model theory notes
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 27, 2010 at 8:32 | comment | added | David Corwin | @John Goodrick: Right, but what I mean is, for a given value of $v_1$, we interpret $d_1$ to be $v_1$? | |
| Jul 27, 2010 at 6:06 | comment | added | Sidney Raffer | A "justification" of this way of speaking is that we can always regard an element of the domain of a structure as a constant symbol that that denotes itself. Hodges mentions this explicitly in his "Model Theory". | |
| Jul 27, 2010 at 2:42 | comment | added | John Goodrick | @Davidac897: Not quite. Remember that an interpretation of a constant in a structure must be an element of that structure, not a variable symbol such as v_1. I see that in the first paragraph of the proof of the CLAIM, Marker is using a standard "abuse of notation" in model theory where the same symbol d_1 is being used both for a new constant symbol added to the language of T, and for the interpretation of this constant in a particular structure. Some other books (e.g. Chang and Keisler) have notation to carefully distinguish these two things, but it looks like Marker's doesn't. | |
| Jul 26, 2010 at 23:30 | vote | accept | David Corwin | ||
| Jul 26, 2010 at 23:05 | comment | added | David Corwin | So you're saying that for each $\bar{v}$, we can apply the new language (i.e. including the $d_i$'s) to this structure by interpreting $d_1$ as $v_1$, etc? I.e. we make a separate application of the language to our structure for each $\bar{v}$. | |
| Jul 26, 2010 at 23:04 | comment | added | David Corwin | So you're saying that for each $\bar{v}$, we can apply the new language (i.e. including the $d_i$'s) to this structure by interpreting $d_1$ as $v_1$, etc? I.e. we make a separate application of the language to our structure for each $\bar{v}$. | |
| Jul 26, 2010 at 22:51 | history | answered | Matti Åstrand | CC BY-SA 2.5 |