Mathematics – Logic
Scientific paper
2012-03-12
Mathematics
Logic
20 pages, no figures. Section 4 split in two sections. Remark 6.3 expanded to cover the 0-dimensional case. All results unchan
Scientific paper
The half-open real unit interval (0,1] is closed under the ordinary multiplication and its residuum. The corresponding infinite-valued propositional logic has as its equivalent algebraic semantics the equational class of cancellative hoops. Fixing a strong unit in a cancellative hoop -equivalently, in the enveloping lattice-ordered abelian group- amounts to fixing a gauge scale for falsity. In this paper we show that any strong unit in a finitely presented cancellative hoop H induces naturally (i.e., in a representation-independent way) an automorphism-invariant positive normalized linear functional on H. Since H is representable as a uniformly dense set of continuous functions on its maximal spectrum, such functionals -in this context usually called states- amount to automorphism-invariant finite Borel measures on the spectrum. Different choices for the unit may be algebraically unrelated (e.g., they may lie in different orbits under the automorphism group of H), but our second main result shows that the corresponding measures are always absolutely continuous w.r.t. each other, and provides an explicit expression for the reciprocal density.
Panti Giovanni
Ravotti Davide
No associations
LandOfFree
Measures induced by units 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 Measures induced by units, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Measures induced by units will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-488483