Measures on finite concrete logics

Abstract

Abstract. We examine the possibility to extend measures and signed measures on a concrete logic on a finite set to those on all its subsets.

Extending States on Finite Concrete Logics

“…2.3 is that it gives the result for group-valued measures for the groups which allow for dividing by 2. Observe in passing that, for instance, the extension problem of course-grained measures as treated in [5] and [10] finds in our opinion the Horn-Tarski criterion an effective proof device (see [3]).…”

“…The logics of X even present a distinguished example of so-called differenceclosed concrete logics. The latter logics were introduced in [10] under the name of symmetric concrete logics. In this note, let us use our notation (in our opinion more suggestive).…”

“…In spite of the progress made by the authors referred to in the abstract above, several questions remain open (see e.g. [10] and [13]). It therefore seems helpful to have the situation clarified in the "testing" case of the logic of even-number-element subsets of a set.…”

On (3,3)-Homogeneous Greechie Orthomodular Posets

“…It is easy to see that n • cardA = m • cardB. Let us recall some definitions of the theory of concrete logics [8], [9]. Let Ω be a set and P(Ω) the Boolean algebra of all subsets of Ω.…”

States on systems of sets that are closed under symmetric difference

“…The notion of the ‐subadditive state seems to first occur in . Some results about ‐subadditive states can be found in , , , , . Let us agree to call a ‐subadditive state simply a state.…”