Reverse mathematics, trichotomy, and dichotomy
By F. G. Dorais, J. L. Hirst and P. Shafer
Journal of Logic and Analysis 4:13 (2012), 1–-14
Using the techniques of reverse mathematics, we analyze the logical strength of statements similar to trichotomy and dichotomy for sequences of reals. Capitalizing on the connection between sequential statements and constructivity, we find computable restrictions of the statements for sequences and constructive restrictions of the original principles.