Timeline for why Skolemization?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 6, 2014 at 19:09 | comment | added | Noah Schweber | @MichaelMcGrady I don't really understand what your comment has to do with Skolemization. Could you elaborate? | |
| Jun 6, 2014 at 18:32 | comment | added | Noah Schweber | Let me just point out that over an arbitrary structure, Skolemization in general is not valid without the axiom of choice. We can think of this as the Skolemization asserting the existence of a very complex object (or collection of objects), which may not live in our model of $ZF$; this is in the same spirit as my answer below. | |
| Jun 6, 2014 at 18:22 | answer | added | Noah Schweber | timeline score: 4 | |
| Jun 6, 2014 at 17:45 | comment | added | Michael McGrady | Underlying the processes is a tension between truth preservation $A~\vdash~B$ and logical truth preservation $\models~A~\iff~\models~B$. I think the question is a good one and that we have not as yet plumbed the depths of what these mean. More work in this area is needed, even though the methodologies have a long track record of usefulness their meaning is yet to be examined. In my opinion, until this is examined thoroughly, the foundations of logic in the 1920-30 period is not well established even yet and all the applications of Cantor's ideas to these formulas are on shaky ground. | |
| Nov 22, 2012 at 1:50 | answer | added | Jason Rute | timeline score: 8 | |
| Nov 21, 2012 at 21:39 | answer | added | Rodrigo Freire | timeline score: 17 | |
| Nov 21, 2012 at 20:12 | comment | added | Suvrit | Some discussion here might be useful: mathoverflow.net/questions/90324/… | |
| Nov 21, 2012 at 19:58 | answer | added | Andreas Blass | timeline score: 13 | |
| Nov 21, 2012 at 19:48 | comment | added | Mohammad Noorani Bakerally | I'm asking, because Skolemization basically means removing existential quantifiers, but why?? | |
| Nov 21, 2012 at 19:14 | comment | added | Tom Leinster | Can you tell us where you've read or heard that keeping existential quantifiers is not good? | |
| Nov 21, 2012 at 17:40 | history | asked | Mohammad Noorani Bakerally | CC BY-SA 3.0 |