Reverse mathematics and uniformity in proofs without excluded middle

Details Reverse mathematics and uniformity in proofs without excluded middle Reverse mathematics and uniformity in proofs without excluded middle

2010-10-25

arxiv.org/abs/1010.5165v1

Notre Dame J. Formal Logic Volume 52, Number 2 (2011), 149-162

Mathematics

Logic

Accepted, Notre Dame Journal of Formal Logic

Scientific paper

10.1215/00294527-1306163

We show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak classical subsystems. In particular, if a $\Pi^1_2$ sentence of a certain form is provable using E-HA${}^\omega$ along with the axiom of choice and an independence of premise principle, the sequential form of the statement is provable in the classical system RCA. We obtain this and similar results using applications of modified realizability and the \textit{Dialectica} interpretation. These results allow us to use techniques of classical reverse mathematics to demonstrate the unprovability of several mathematical principles in subsystems of constructive analysis.

Affiliated with

Also associated with

No associations

Rating

Reverse mathematics and uniformity in proofs without excluded middle does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Reverse mathematics and uniformity in proofs without excluded middle, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reverse mathematics and uniformity in proofs without excluded middle will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-94358