Determined Admissible 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 ...

Presentations of Structures in Admissible Sets

We consider copies and constructivizations of structures in admissible sets. It is well known that in classical computable model theory (on natural numbers) these approaches are equivalent: a structure has computable (decidable) copy if and only if it is constructivizable (strongly constructivizable). However, in admissible sets the "if" part of this statement is not true in general. In the rst...

Counting Lattice Points in Admissible Adelic Sets