[FOM] Two questions about Peano arithmetic
David Isles
dkisles at gmail.com
Sun Apr 8 19:18:44 EDT 2012
I would appreciate any help on the following two questions:
1. Within a first-order system of Peano arithmetic, such as that given
in Kleene’s book, which includes function constants only for ‘ (successor),
+ (addition), and x (multiplication), is there a proof different from the
obvious one (his Theorem 157) which shows the existence of a common
multiple of the integers in the sequence 1,2,...,n for any n?
2. Is it possible in a system of Peano arithmetic as described in
Question 1, to formalize the theory of the beta-function (Kleene page 44,
Remark 1) without having proved the existence of a common multiple of the
integers in the sequence 1,2,...,n for any n?
Thanks, David Isles
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