[FOM] I\Sigma_1 + Con(I\Sigma_1)

Richard Heck richard_heck at brown.edu
Fri Aug 23 14:52:12 EDT 2013

Obviously, I\Sigma_1 + Con(I\Sigma_1) is a sub-theory of I\Sigma_2, 
since I\Sigma_2 proves Con(I\Sigma_1). I am guessing (a) that it is a 
proper sub-theory and (b) that it does not even interpret I\Sigma_2. 
Yes? References?

Does the same hold for I\Sigma_n + Con(I\Sigma_{n+k})?

Thanks in advance,
Richard Heck

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