In 1969, Per Lindstrom proved his celebrated theorem characterising the
first-order logic and established criteria for the first-order definability of
formal theories for discrete structures. K. J. Barwise, S. Shelah, J. Vaananen
and others extended Lindstrom's characterizability program to classes of
infinitary logic systems, including a recent paper by M. Dzamonja and J.
Vaananen on Karp's chain logic, which satisfies interpolation, undefinability
of well-order, and is maximal in the class of logic systems with these
properties. The novelty of the chain logic is in its new definition of
satisfability. In our paper, we give a framework for Lindstrom's type
characterizability of predicate logic systems interpreted semantically in
models with objects based on measures (analytic structures). In particular,
Hajek's Logic of Integral is redefined as an abstract logic with a new type of
Hajek's satisfiability and constitutes a maximal logic in the class of logic
systems for describing analytic structures with Lebesgue integrals and
satisfying compactness, elementary chain condition, and weak negation.

该论文主要探讨了一些逻辑系统及其特性，包括一种基于度量（解析结构）的谓词逻辑系统，其定义了一种新型满足性，是描述具有勒贝格积分和满足紧致性，基本链条件和弱否定的解析结构的逻辑系统中的极大系统。