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3:59 PM
I remember reading somewhere that every theory $T$ in a language $L$ has QE in a bigger language $L'\supseteq L$, but I don't remember where, does someone have a reference?
 
4:12 PM
Found it, one also needs to extend $T$ though
 
 
2 hours later…
6:24 PM
@AlessandroCodenotti Basically you skolemize, right?
@LeakyNun Without set theory or at least something that can talk about collections, what does "model" even mean? =D
 
6:39 PM
@user21820 I don't know what that means
But basically for all formulas phi in N free variables you add an N-ary relation symbol R_phi, and add to T a universal closure of the formula phi<---->R_phi
Iterate countably many times
 
Hmm that sounds very different.
 
What did you have in mind? I'm interested in different approaches
 
I'm tired now though so I can't think straight, but what I meant by skolemize is that you create new function-symbols to witness all the provable existentials.
And iterate to close it up.
 
My first idea was also to add witnesses
(Probably because we saw the Henkin construction in class)
 
Yea it doesn't work?
 
6:44 PM
I think it does, but I haven't thought about the details
 
Oh okay. If you find out that it doesn't, let me know! Otherwise I'll have this wrong idea stuck in my head haha..
 
Sure, I'll think about it
 
By the way, @AlessandroCodenotti @LeakyNun @shredalert @famesyasd: Here's an interesting puzzle question:
> Put n red stones then n green stones then n blue stones on a ring. At each step you can take any stone and hop it over a pair of adjacent stones of the same colour, in any direction around the ring. So for example, if you have ...rbb... then you can take the r stone and hop it over the bb pair. The question is: For what n is there a sequence of steps that rearranges the stones to be blue then green then red?
 
 
2 hours later…
8:38 PM
@user21820 I did not understand the conditions. Consider ...rbgrbgrbg... . There are no two adjacent stone of the same colour so no stone can be moved and it is not of the form ...rrr...bbb...ggg...
 

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