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# logic, compactness theorem watch

1. Q9 - http://www.dpmms.cam.ac.uk/site2002/...ogic2010-1.pdf

for example, why can we not have valuations v_n that are zero except for v_n (t_n) = 1 ?

then certainly the n cannot be bounded by N, since v_(N+1) would be zero on all of {t_1, ..., t_N}...
2. (Original post by Chewwy)
Q9 - http://www.dpmms.cam.ac.uk/site2002/...ogic2010-1.pdf

for example, why can we not have valuations v_n that are zero except for v_n (t_n) = 1 ?

then certainly the n cannot be bounded by N, since v_(N+1) would be zero on all of {t_1, ..., t_N}...
It follows quickly from noting that V_n is 0 E R
moreover the bijection of the above can cause subjection by making an inspection on the assumption that the above can cause an inflammation which can cause rejection from a interjection
3. You haven't read the question properly. For every valuation v we must have one of these t_n being true. This puts a restriction on t_n.
4. Here's a hint, but it might be nonsense, because I haven't thought about the question much...

Spoiler:
Show
Try and build a valuation v with v(t_i) = 0 for all i recursively: if possible, set v(t_1) = 0 (if not, stop, you're done). Then, if possible, set v(t_2) = 0, etc. At some point this must fail, i.e. if v(t_i) = 0 for all 1 <= i <= k-1, we must have v(t_k) = 1. Then...

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