[FOM] question about Mendelson's Intro to Math Logic

Robert Solovay solovay at gmail.com
Wed Feb 12 00:41:13 EST 2014


Can you state the problem in question fully and precisely.  I don't have
access to Mendelson and your description is not detailed enough for me to
think about your question.

-- Bob Solovay
On Feb 11, 2014 3:02 PM, "Robert Lubarsky" <Lubarsky.Robert at comcast.net>

> There's an exercise from Mendelson's Intro to Mathematical Logic that I
> cannot do, and would like an answer to. In the 5th edition, it's 1.59 on
> p. 39. Namely, he gives three axioms for a Hilbert-style propositional
> proof system. The first two are essentially the combinators s and k. The
> third is
> (not C -> not B) -> [ (not C -> B) -> C ]. The exercise in question is to
> show that, if you replace this last schema with (not B -> not C) -> (B ->
> C) then the new system proves the same as the old. I don't see how to do
> this.
> My attempt is as follows. We can use the deduction theorem. So assume (not
> C -> not B) and (not C -> B), with the goal of proving C. From the new
> schema, we get  B -> C. We can compose that with (not C -> B) to get (not C
> -> C). I don't see how to go from that to C within this system.
> Bob Lubarsky
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