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.

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.

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].

We used a response competition paradigm to investigate whether a distractor is effectively rejected under conditions where it is projected to a highly-loaded hemisphere. In two experiments we asked right-handed participants to identify a target among five task-relevant letters while they ignored a distractor. We manipulated both the distractor visual-field and the compatibility of the target and the distractor. In the low-loaded visual-field, we presented a distractor with one task-relevant stimulus to one visual-field and the remaining task-relevant stimuli to the (...) opposite visual-field. In the high-loaded visual-field, we presented a distractor and task-relevant stimuli in reverse. In Experiment 1 , we found a compatibility effect for the low-loaded, but not for the high-loaded visual-field. In Experiment 2, this modulation of the compatibility effect did not appear when the upper/lower visual-field was manipulated. These findings demonstrate that a distractor is successfully ignored when it is presented to a highly-loaded hemisphere. (shrink)

When the Argonauts reach the island of Lemnos, Apollonius of Rhodes tells us, they send their herald Aethalides to the ruler of the island. Such a means of establishing contact and requesting safe passage was the norm in the Homeric world; there heralds acted as intermediaries between commanders and subordinates or between groups of people. In preliterate societies, heralds facilitated communication: messages were transmitted through memorization and repetition rather than by means of writing. While verbatim repetition was no doubt a (...) necessary feature of this form of communication, its wholesale transference into Homeric poetry was not necessarily the logical corollary. Nonetheless, we know of such repetitions precisely because of their appearance in the Homeric poems. It is now widely accepted that such passages are a result of the oral style of composition in which the oral poet repeats passages just as he uses shorter formulaic phrases. The debate embedded in the A-scholia of the Iliad suggests that repeated passages were a source of contention already in antiquity. While it is more common to see the scholiasts trying to decide which passage is ‘correct’ and which should be athetized, this provides evidence that athetization was not a unanimous impulse. The scholiast defends 2.60–71, part of which is repeated for the third time, against Zenodotus. (shrink)

This essay is one of three responses to Casper Bruun Jensen's article “Experiments in Good Faith and Hopefulness: Toward a Postcritical Social Science,” published in the Spring 2014 issue of Common Knowledge. Jensen suggested that the postcritical mode of knowledge production should focus on a continuous and persistent analytical effort to resist despair by “insisting properly.” This commentary, by one of three authors on whom the original article focused, contrasts Jensen's emphasis on insistence with the idea of ethnography as response. (...) The reconceptualization of ethnographic work as response can have various and divergent consequences, some of which are explored here with reference to the author's own ethnographic research on indigenous Fijian gift-giving and Japanese financial trading. While his immediate interest here is to expose differences in the kinds of openness that insistence and response afford, he concludes that willingness to respond is more basic to anthropology than the ethnographer's cultivation of the internal strength required to keep anthropology going as an enterprise. (shrink)

Obtaining informed consent is a cornerstone of biomedical research, yet participants comprehension of presented information is often low. The most effective interventions to improve understanding rates have not been identified.