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. 2010 Mathematics Subject Classification 03B...

Some recent work of Gross and Prasad [14] suggests that the root numbers attached to certain symplectic representations of the Weil-Deligne group of a local field F control certain branching rules for representations of orthogonal groups over F . On a global level, this local phenomenon should have implications for the structure of the value at the center of symmetry for certain L-functions of ...

For a digraph H, the Constraint Satisfaction Problem with template H, or CSP(H), is the problem of deciding whether a given input digraph G admits a homomorphism to H. The CSP dichotomy conjecture of Feder and Vardi states that for any digraph H, CSP(H) is either in P or NP-complete. Barto, Kozik, Maróti and Niven (Proc. Amer. Math. Soc, 2009) confirmed the conjecture for a class of oriented tr...

We consider the problem of finding a homomorphism from an input digraph G to a fixed digraph H. We show that if H admits a weak-near-unanimity polymorphism φ then deciding whether G admits a homomorphism to H (HOM(H)) is polynomial time solvable. This confirms the conjecture of Bulatov, Jeavons, and Krokhin [BJK05], in the form postulated by Maroti and McKenzie [MM08], and consequently implies ...