Tagged Questions
5
votes
2answers
207 views
Primes in nonstandard models of PA
What is known about prime numbers in nonstandard models of PA?
Restricted to true natural numbers the sets are identical, but does there always exist nonstandard primes? Can we explicitly define one ...
3
votes
2answers
159 views
What does a nonstandard proof of Con(PA) look like?
As in Godel's incompleteness theorem natural numbers encode proofs of theorems. Due to Godel's completeness theorem there is a natural number (in some nonstandard model) that proves $Con(PA)$.
What ...
10
votes
1answer
768 views
Non-standard models of arithmetic for Dummies
Why is (1) a copy of $\mathbb{N}$ "followed by" a copy of $\mathbb{Z}$ not a (non-standard) model of arithmetic, neither (2) a copy of $\mathbb{N}$ followed by an infinite sequence of copies of ...
