Hi everyone,
Help Session, Thursday July 2, 1pm-3pm, Room 204, K17 Building : )
All best,
Seb
Hi everyone,
A quick note on infinite trees and how to specifiy a countermodel.
An infinite tree is one that forces us to add new constants via existential quantifier elimination during our attempt to saturate an open path. Here is an example (using `Ex' for the existential quantifier):
Suppose that you have a tree with
EyRay
on an open branch, and you eliminate the existential quantifer getting
Rab
Suppose also that in an attempt to saturatrate this open path that you ended up with another instance of hte same existential quantifer, this time as follows:
EyRby
which you eliminate again, getting this time
Rbc
and so on and on....
Even with only two iterations of exitential quantifier elimination, it is obvious that the next one will be
EyRcy
from which you will get
Rcd
and then Rde, and then Ref, Rfg, Rgh, Rhi....
and so on infinitely.
In this case the domain D of your countermodel will need infinitely many objects D : {1, 2, 3, 4, 5, 6, 7, 8, 9....}, and infinitely many names with the appropriate mappings to objects in D - a:1, b:2, c:3, d:4, e:5, f:6, g:7, h:8, I:9....
Given the instances of R in the open path above, you can specify the extension of R as follows:
R : { <1, 2>, <2, 3>, <3, 4>, <4, 5>....}
And then you are done.
Good luck with Assignment 2!
All best,
Seb
Dear denizens of COMP2111,
Thank you so much for being awesome, and for making the very first iteration of the new version of COMP2111 so fantastic. You are the best! Thank you for your excellent questions, thank you for being so genuinely interested in the topic, and thank you for all of your hard work so far and for the rest of the term.
Next stop...Vineet! I shall be there on Thursday also and I am looking very forward.
All best,
Seb