Meier (2012) gave a "mathematical logic foundation" of the purely measurable universal type space (Heifetz and Samet, 1998). The mathematical logic foundation, however, discloses an inconsistency in the type space literature: a finitary language is used for the belief hierarchies and an...

Meier (2012) gave a "mathematical logic foundation" of the purely measurable universal type space (Heifetz and Samet, 1998). The mathematical logic foundation, however, discloses an inconsistency in the type space literature: a finitary language is used for the belief hierarchies and an...

We continue the work of Aumann (Ann. Statist. 4 (1976), 1236-1239), Geanakoplos and Polemarchakis (J. Econ. Theory 28 (1982), 192-200) on common knowledge and consensus, reconsidering the arguments and the findings of both Aumann (1976) and Geanakoplos and Polemarchakis (1982) and offering...

Following from Tarbush (2011a), we explore the implications of using two different definitions of informativeness over kens; one that ranks objective, and the other subjective information. With the first, we create a new semantic operation that allows us to derive agreement theorems even when...

We develop a framework that allows us to reproduce the generalised agreement theorem of Samet (2010), and extend it to models with a non-partitional information structure, while highlighting the features that distinguish the result from the classic theorems found in the literature. Furthermore,...

We present an extension of Aumann's Agreement Theorem to the case of multiple priors. If agents update all their priors, then, for the Agreement Theorem to hold, it is sufficient to assume that they have closed, connected and intersecting sets of priors. On the other hand, if agents select the...

An example is given in which agents agree to disagree, showing that Aumann's (1976) Agreement Theorem does not extend to a countable space of equiprobable states of nature. Even in this unorthodox setting, if the sets of the information partitions are intervals, an agreement theorem holds. A...