[FOM] Iterating under Con(T)

joeshipman@aol.com joeshipman at aol.com
Fri Mar 10 14:07:23 EST 2006


>To make the question more precise, define the following sequence of
>theories by transfinite recursion:
>T_0 = PA
>T_{k+1} = T_k + Con(T_k)
>T_l = \cup_{k<l} T_k, for l a limit

This is not really a definition. Eventually there will be a limit 
ordinal k for which there is no canonical statement Con(T_k), so you 
won't be able to define T_(k+1).

Also, shouldn't you be closing each step under logical implication? 
Otherwise your T_i are not "theories".

-- JS

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