I need help in the following problem:
Let be a (first order) language. Find -fomulae that for any -structure with support :
.
Some ideas: Because the signature is empty, there are no relations, no functions and no constants. The only possible formulae consist of terms like with variables and the logical signs (,), (others excluded by demand).
For I guess something like:
but this seems quite complex. Is there a shorter form? Or is it even correct? And the others?
yes, of course. I used copy-paste instead of brain.
yes, thanks. what I wrote is not consequent with the above. If you put -quantor for in front of the second conjunction part, then the proof is easy.In this formula, the variables are not bound.
But, I hope, it works with the unbound variables as well! Because then, the modelling requires -quantor for and after using the induction assumption for , it can be shown that:
What do you think? I just started learning logic, so I try to become familiar with all this.
Yes, but the text is in German. The exercise is here http://www.math.uni-heidelberg.de/lo...thlogik_05.pdf and the solution on page 6 here http://www.math.uni-heidelberg.de/lo...k/handout4.pdf . I hope it helps.
Thanks. Sadly, I don't read German. So I could be staring at the title of the textbook at either one of the links you provided and
not even realize it. Can you just provide the title of the textbook and the author(s)? Presumably, it's a book on mathematical logic.
Perhaps it's been translated into English.
By the way, is Klaus Ambos-Spies your professor?
I asked about him becauce his name is on the front page of the first link that you kindly provided. You didn't see it?
Naturally, I connected his name with the document and thus the problem.
Is he famous? I don't know. You tell me.
Am I amused by his name? No. Maybe your question was meant to be amusing.
Adios.