[FOM] Query on independence results and constructive theories

praatika@mappi.helsinki.fi praatika at mappi.helsinki.fi
Sat Dec 16 03:45:00 EST 2006

I tried this query some time ago here, without any success. Here it is 
again, a bit more exactly:

(1) If I don't remember wrong, at least some time ago, Delta-1-2 CA (or 
something like it) was the strongest theory which could be constructively 
justified. Is this still the state of affairs?

(2) Now Finite Krusakal's Theorem (and extended KT, and such) are not 
provable in predicatively justifiable theories, but are they still 
provable in a theory that is constructively justifable?

(3) Are there any neat examples of theorems which are independent of 
Delta-1-2 CA, or whatever theories which are, today, known to be 
constructively acceptable? 

(4) If there is, is the proof of independence itself constructive?


Panu Raatikainen
Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy
Department of Philosophy
University of Helsinki
E-mail: panu.raatikainen at helsinki.fi

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