In this paper we study a certain class of Lie algebras over commutative von Neumann algebras satisfying a certain finiteness condition. By using Boolean valued methods developed by Takeuti [8]-[11], we will establish the basic structure and representation theorems.

Just as Kaplansky [4] has introduced the notion of an AW*-module as a generalization of a complex Hilbert space, we introduce the notion of an AL*-algebra, which is a generalization of that of an L*-algebra invented by Schue [9, 10]. By using Boolean valued methods developed by Ozawa [6–8], Takeuti [11–13] and others, we establish its basic properties including a fundamental structure theorem. This paper should be regarded as a continuation or our previous paper [5], the familiarity with which is (...) presupposed. MSC: 03C90, 03E40, 17B65, 46L10. (shrink)

In conventional generalization of the main results of classical measure theory to Stone algebra valued measures, the values that measures and functions can take are Booleanized, while the classical notion of a σ-field is retained. The main purpose of this paper is to show by abundace of illustrations that if we agree to Booleanize the notion of a σ-field as well, then all the glorious legacy of classical measure theory is preserved completely.

In spite of the philosophical significance of higher-order modal logic, the modal logician's main concern has been with sentential logic. In this paper we do not intend to go into philosophical details, but we only remark that higher-order modal logic has a close relationship with Montague's well-known idea of “universal grammar”, which is an ambitious attempt to build a logical theory of natural languages with exact syntax and semantics, comparable with the artificial languages of mathematical logic. For this matter, the (...) reader can consult, e.g., Montague [8], [9] and Gallin [2]. (shrink)

The aims of this paper are: (1) to present tense-logical versions of such classical notions as saturated and special models; (2) to establish several fundamental existence theorems about these notions; (3) to apply these powerful techniques to tense complexity.In this paper we are concerned exclusively with quantifiedK 1 (for linear time) with constant domain. Our present research owes much to Bowen [2], Fine [5] and Gabbay [6].

By creating an unbounded topological reduction theory for complex Hilbert spaces over Stonean spaces, we can give a category-theoretic duality between Boolean valued analysis and topological reduction theory for complex Hilbert spaces. MSC: 03C90, 03E40, 06E15, 46M99.

HIV stigma and fears surrounding the disease pose a challenge for public health interventions, particularly those that target pregnant women. In order to reduce stigma and improve the lives of vulnerable populations, researchers have recognized a need to integrate different types of support at various levels. To better inform HIV interventions, the current study draws on social-ecological and evolutionary theories of reproduction to predict stigma and fear of contracting HIV among pregnant women in South India. The aims of this study (...) were twofold: compare the social-ecological model to a modified maternal-fetal protection model and test a combined model that included strong predictors from each model. The study took place in 2008–2011 in Mysore District, Karnataka, India. Using data from a cross-sectional survey and biological indicators of health, we statistically modeled social-ecological variables representing individual, interpersonal, and community/institutional levels. Participants were 645 pregnant women. The social-ecological and combined models were the best-fitting models for HIV-related stigma, and the combined model was the best fit for HIV-related fear. Our findings suggest that combining reproductive life history factors along with individual, interpersonal, and community/institutional factors are significant indicators of HIV-related stigma and fear. Results of this study support a multifaceted approach to intervention development for HIV-related stigma and fear. The combined model in this study can be used as a predictive model for future research focused on HIV stigma and fear, with the intent that dual consideration of social-ecological and evolutionary theories will improve public health communication efforts. (shrink)