In 1981, Takeuti introduced quantum set theory as the quantum counterpart of Boolean valued models of set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed subspaces in a Hilbert space and showed that appropriate quantum counterparts of ZFC axioms hold in the model. Here, Takeuti's formulation is extended to construct a model of set theory based on the logic represented by the lattice of projections in an arbitrary von Neumann algebra. (...) A transfer principle is established that enables us to transfer theorems of ZFC to their quantum counterparts holding in the model. The set of real numbers in the model is shown to be in one-to-one correspondence with the set of self-adjoint operators affiliated with the von Neumann algebra generated by the logic. Despite the difficulty pointed out by Takeuti that equality axioms do not generally hold in quantum set theory, it is shown that equality axioms hold for any real numbers in the model. It is also shown that any observational proposition in quantum mechanics can be represented by a corresponding statement for real numbers in the model with the truth value consistent with the standard formulation of quantum mechanics, and that the equality relation between two real numbers in the model is equivalent with the notion of perfect correlation between corresponding observables (self-adjoint operators) in quantum mechanics. The paper is concluded with some remarks on the relevance to quantum set theory of the choice of the implication connective in quantum logic. (shrink)

In 1981, Takeuti introduced quantum set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed linear subspaces of a Hilbert space in a manner analogous to Boolean-valued models of set theory, and showed that appropriate counterparts of the axioms of Zermelo–Fraenkel set theory with the axiom of choice hold in the model. In this paper, we aim at unifying Takeuti’s model with Boolean-valued models by constructing models based on general complete orthomodular (...) lattices, and generalizing the transfer principle in Boolean-valued models, which asserts that every theorem in ZFC set theory holds in the models, to a general form holding in every orthomodular-valued model. One of the central problems in this program is the well-known arbitrariness in choosing a binary operation for implication. To clarify what properties are required to obtain the generalized transfer principle, we introduce a class of binary operations extending the implication on Boolean logic, called generalized implications, including even nonpolynomially definable operations. We study the properties of those operations in detail and show that all of them admit the generalized transfer principle. Moreover, we determine all the polynomially definable operations for which the generalized transfer principle holds. This result allows us to abandon the Sasaki arrow originally assumed for Takeuti’s model and leads to a much more flexible approach to quantum set theory. (shrink)

I‐J has been regarded as a polymorphic genetic marker controlled by a locus in the major histocompatibility complex (MHC) which is expressed only on functional T cells. However, this antigenic determinant has been found not to be directly encoded by the MHC gene per se but is somatically generated according to the MHC of the cellular environment during ontogeny. This explains the apparent linkage of I‐J to MHC, despite the failure to find the structural gene for I‐J within the MHC. (...) The I‐J paradox provides an instance of a polymorphism that does not follow the standard genetics of Mendelian structural genes. (shrink)

Quantum set theory and topos quantum theory are two long running projects in the mathematical foundations of quantum mechanics that share a great deal of conceptual and technical affinity. Most pertinently, both approaches attempt to resolve some of the conceptual difficulties surrounding QM by reformulating parts of the theory inside of nonclassical mathematical universes, albeit with very different internal logics. We call such mathematical universes, together with those mathematical and logical structures within them that are pertinent to the physical interpretation, (...) ‘Q-worlds’. Here, we provide a unifying framework that allows us to better understand the relationship between different Q-worlds, and define a general method for transferring concepts and results between TQT and QST, thereby significantly increasing the expressive power of both approaches. Along the way, we develop a novel connection to paraconsistent logic and introduce a new class of structures that have significant implications for recent work on paraconsistent set theory. (shrink)

The recently established universal uncertainty principle revealed that two nowhere commuting observables can be measured simultaneously in some state, whereas they have no joint probability distribution in any state. Thus, one measuring apparatus can simultaneously measure two observables that have no simultaneous reality. In order to reconcile this discrepancy, an approach based on quantum logic is proposed to establish the relation between quantum reality and measurement. We provide a language speaking of values of observables independent of measurement based on quantum (...) logic and we construct in this language the state-dependent notions of joint determinateness, value identity, and simultaneous measurability. This naturally provides a contextual interpretation, in which we can safely claim such a statement that one measuring apparatus measures one observable in one context and simultaneously it measures another nowhere commuting observable in another incompatible context. (shrink)

Western sociology of the body, despite its attempt to create a somatic approach to human existence, inevitably shares many of the rationalistic and Cartesian assumptions of wider Western sociology. A contrasting, and in many ways radically different approach is that found in both classical and contemporary Japanese thought. In this article two major contemporary Japanese theorists of the body - Ichikawa Hiroshi and Yuasa Yasuo - are introduced and their work examined as distinctive, and in the West virtually unknown, contributions (...) to body analysis. Their views are briefly contrasted with some of the major themes of Western, and in particular British, sociology of the body and the implications of their work for future investigation of the human body are sketched out. (shrink)

A nonstandard universe is constructed from a superstructure in a Boolean-valued model of set theory. This provides a new framework of nonstandard analysis with which methods of forcing are incorporated naturally. Various new principles in this framework are provided together with the following applications: An example of an 1-saturated Boolean ultrapower of the real number field which is not Scott complete is constructed. Infinitesimal analysis based on the generic extension of the hyperreal numbers is provided, and the hull completeness theorem (...) and the Loeb measure construction are extended to objects in the generic extension of the internal universe. The reduction theory of the Boolean-valued complex numbers are developed as a prototype of the applications to the topological reduction theory of Boolean sheaves or operator algebras. (shrink)

The emotions that people experience in day-to-day social situations are often mixed emotions. Although autobiographical recall is useful as an emotion induction procedure, it often involves recalling memories associated with a specific discrete emotion. However, real-life emotions occur freely and spontaneously, without such constraints. To understand real-life emotions, the present study examined characteristics of emotions that were elicited by recalling “stressful interpersonal events in daily life” without the targeted evocation of a specific discrete emotion. Assuming generation of mixed and complex (...) emotions, emotional groups with relatively strong correlation of multiple emotions according to surprise, fear, anger, disgust, sadness, and happiness were expected. Seventy-two university students participated in the study. In the emotion induction procedure, participants freely recalled memories as per the instructions on a monitor, and then responded silently to a series of questions concerning any one recalled incident. Assessments of emotional states using emotion scales and another item indicated that validated emotional changes had occurred during the task. Inter-correlations between six emotions demonstrated an emotional group consisting of disgust and anger, which frequently occur as negative interpersonal feelings, and that of fear and sadness. This indicated generation of mixed and complex emotions as experienced in social life. Future studies concerning relationships between these emotions and other factors, including neurophysiological responses, may facilitate further understanding about relationships between mental and physiological processes occurring in daily life. (shrink)

The cytoplasmic domain of the cell adhesion molecule uvomorulin associates with three independent proteins, named catenins, which are structurally related in different cell types of various species. This complex formation connects uvnomorulin and cytoskeletal structures and might, moreover, be involved in other adhesion‐dependent mechanisms.

The model of mind and body in Tibetan medical practice is based on Buddhist theory, and is neither dualistic in a Cartesian sense, nor monistic. Rather, it represents a genuine alternative to these positions by presenting mind/body interaction as a dynamic process that is situated within the context of the individual’s relationships with others and the environment. Due to the distinctiveness, yet interdependence, of mind and body, the physician’s task is to heal the patient’s mind (blo-gso) as well as body. (...) This in turn emphasizes the central importance of ‘compassion’ in the physician/patient relationship. This article investigates how Tibetan medical practitioners understand and enact the mind/ body and physician/patient relationships, and how this relates to theoretical explications of these relationships in Tibetan medical and Buddhist teachings. Furthermore, Tibetan medicine provides an interesting model for comparison with embodied theories of cognition, which see consciousness, the body and its environment as integral parts of a complex, dynamical cognitive system. (shrink)

An ordered field is said to be Scott complete iff it is complete with respect to its uniform structure. Zakon has asked whether nonstandard real lines are Scott complete. We prove in ZFC that for any complete Boolean algebra B which is not (ω, 2)-distributive there is an ultrafilter U of B such that the Boolean ultrapower of the real line modulo U is not Scott complete. We also show how forcing in set theory gives rise to examples of Boolean (...) ultrapowers of the real line which are not Scott complete. (shrink)

Halvorson and Clifton have given a mathematical reconstruction of Bohr’s reply to Einstein, Podolsky and Rosen (EPR), and argued that this reply is dictated by the two requirements of classicality and objectivity for the description of experimental data, by proving consistency between their objectivity requirement and a contextualized version of the EPR reality criterion which had been introduced by Howard in his earlier analysis of Bohr’s reply. In the present paper, we generalize the above consistency theorem, with a rather elementary (...) proof, to a general formulation of EPR states applicable to both non-relativistic quantum mechanics and algebraic quantum field theory; and we clarify the elements of reality in EPR states in terms of Bohr’s requirements of classicality and objectivity, in a general formulation of algebraic quantum theory. (shrink)

Long time delay before lasing in a II-VI laser diode has been observed. Due to this delay, a nominal threshold current increases as the width of applied current pulse becomes shorter. This delay is attributed to the internal Q switching caused by the balance of injected carriers, temperature rise and gain-guiding. By fitting the calculated data to the experimental ones, rates of refractive index change with carrier concentration and with temperature have been estimated.

In quantum logic, introduced by Birkhoff and von Neumann, De Morgan's Laws play an important role in the projection-valued truth value assignment of observational propositions in quantum mechanics. Takeuti's quantum set theory extends this assignment to all the set-theoretical statements on the universe of quantum sets. However, Takeuti's quantum set theory has a problem in that De Morgan's Laws do not hold between universal and existential bounded quantifiers. Here, we solve this problem by introducing a new truth value assignment for (...) bounded quantifiers that satisfies De Morgan's Laws. To justify the new assignment, we prove the Transfer Principle, showing that this assignment of a truth value to every bounded ZFC theorem has a lower bound determined by the commutator, a projection-valued degree of commutativity, of constants in the formula. We study the most general class of truth value assignments and obtain necessary and sufficient conditions for them to satisfy the Transfer Principle, to satisfy De Morgan's Laws, and to satisfy both. For the class of assignments with polynomially definable logical operations, we determine exactly 36 assignments that satisfy the Transfer Principle and exactly 6 assignments that satisfy both the Transfer Principle and De Morgan's Laws. (shrink)