The Omega Rule is $\mathbf{Π_{1}^{1}}$-Complete in the $λβ$-Calculus

Details The Omega Rule is $\mathbf{Π_{1}^{1}}$-Complete in the $λβ$-Calculus The Omega Rule is $\mathbf{Π_{1}^{1}}$-Complete in the $λβ$-Calculus

2009-03-07

arxiv.org/abs/0903.1374v2

Computer Science

Logic in Computer Science

Scientific paper

In a functional calculus, the so called \Omega-rule states that if two terms P and Q applied to any closed term N return the same value (i.e. PN = QN), then they are equal (i.e. P = Q holds). As it is well known, in the \lambda\beta-calculus the \Omega-rule does not hold, even when the \eta-rule (weak extensionality) is added to the calculus. A long-standing problem of H. Barendregt (1975) concerns the determination of the logical power of the \Omega-rule when added to the \lambda\beta-calculus. In this paper we solve the problem, by showing that the resulting theory is \Pi\_{1}^{1}-complete.

Affiliated with

Also associated with

No associations

Rating

The Omega Rule is $\mathbf{Π_{1}^{1}}$-Complete in the $λβ$-Calculus 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 The Omega Rule is $\mathbf{Π_{1}^{1}}$-Complete in the $λβ$-Calculus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Omega Rule is $\mathbf{Π_{1}^{1}}$-Complete in the $λβ$-Calculus will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-496278