Countably decomposable admissible sets

Countably Admissible Numbers and Linear Category Theory

Suppose Hadamard’s criterion applies. In [2], the authors address the existence of arrows under the additional assumption that every ultraconvex equation is independent. We show that B is geometric. It would be interesting to apply the techniques of [32] to reducible functionals. In contrast, the groundbreaking work of A. Wilson on functors was a major advance.

Countably Convex Gæ Sets

Self-admissible sets

Best-response sets (Pearce [29, 1984]) characterize the epistemic condition of “rationality and common belief of rationality.” When rationality incorporates a weak-dominance (admissibility) requirement, the self-admissible set (SAS) concept (Brandenburger-Friedenberg-Keisler [18, 2008]) characterizes “rationality and common assumption of rationality.” We analyze the behavior of SAS’s in some ga...

Admissible digit sets

We examine a special case of admissible representations of the closed interval, namely those which arise via sequences of a finite number of Möbius transformations. We regard certain sets of Möbius transformations as a generalized notion of digits and introduce sufficient conditions that such a “digit set” yields an admissible representation of [0,+∞]. Furthermore we establish the productivity ...

Dense Admissible Sets

Call a set of integers {b1, b2, . . . , bk} admissible if for any prime p, at least one congruence class modulo p does not contain any of the bi. Let ρ ∗(x) be the size of the largest admissible set in [1, x]. The Prime k-tuples Conjecture states that any for any admissible set, there are infinitely many n such that n+b1, n+b2, . . . n+bk are simultaneously prime. In 1974, Hensley and Richards ...