Rank Of A Set Research Articles

Computation and Hypercomputation

This paper shows some of the differences and similarities between computation and hypercomputation, the similarities relating to the complexity of propositional computation and the differences being the propositions that can be decided computationally or hypercomputationally. The methods used are ordinal Turing machines with infinitely long programs and diagonalization out of computing complexity classes. The main results are the characterization of inequalities of run time complexities of serial, indeterministic serial and parallel computers and hypercomputers and the specification of a hierarchy of hypercomputers that can hypercompute the truths of all propositions in the standard class model of set theory, the von Neumann hierarchy of pure sets.

Cinderella of the south seas? Virtuous victims, empowerment and other fables of development feminism

The developmental logic underpinning ‘Cinderella projects,’ in which women of the Global South are targeted for interventions intended to tap and expand their unrecognized economic and entrepreneurial potential. This version of ‘development feminism,’ constructs its female objects as both impoverished victim-subjects and as nascent market-oriented actors. Moreover, development feminist discourse, grounded as it is in seemingly universal ideas of women’s oppression, equality and economic participation, generates paradoxical effects in different social contexts. Drawing on ethnographic examples from Polynesia, the paper illustrates how a homogeneous concept of ‘woman’ makes little sense because local gender categories are complexly intersected by age, socio-economic status as well as by hereditary rank. As a result, development feminisms’ gender interventions transform local individual subjectivities in novel and often unexpected ways, producing new forms of inequality while obscuring others.

Empirically based developmental and behavioral intervention programs targeting the core symptoms and language development in toddlers and preschool children with autism spectrum disorder

Empirically based developmental and behavioral intervention programs targeting the core symptoms and language development in toddlers and preschool children with autism spectrum disorder Abstract. This systematic review summarizes findings of articles included in the German AWMF-S3 clinical guideline on early intervention in autism spectrum disorders (ASD). We present the current state-of the art of evidence-based interventions for toddlers and preschool-aged children with ASD, specifically targeting the core symptoms and language development. We included studies on manualized developmental and behavioral interventions for children with ASD aged <7 years according to DSM-III(R), DSM-IV(TR), DSM-5, and ICD-10. The publication dates ranged from 1 January 2011 to 31 August 2018 or as included in the NICE-children guidelines. Studies were included by an iterative hierarchy: systematic review > randomized-controlled trial > clinically controlled trial. Outcome measures were core ASD symptoms and precursor abilities, or language abilities. The interventions were collated by (1) frequency and (2) approach. The studies focused on low-intensive interventions targeting parental synchrony, the child's initiations, reciprocity, joint attention, play and imitation skills as well as comprehensive interventions. Improvement of core ASD symptoms regarding social communication was observed for low-intensive training of parental synchrony and child's reciprocity as well as for low-intensive comprehensive developmental interventions implementing natural-learning paradigms. High-frequency discrete trial interventions did not improve social communication. Language abilities improved by comprehensive interventions. In conclusion, intervention recommendations are summarized.

“Many Seasons Ago”: Slavery and Its Rejection among Foragers on the Pacific Coast of North America

ABSTRACTAnthropologists have traditionally classified foragers on the Pacific coast of North America into two major culture areas, characterized by strikingly different social and ethical systems. These are “California” and the adjacent “Northwest Coast.” Foragers in the northern part of California exhibit many elements of Weber's “Protestant ethic,” such as the moral injunction for community leaders to work hard, seek spiritual purpose by introspection, and pursue monetary wealth while avoiding material excess. By contrast, the social organization of Northwest Coast foragers bears comparison with that of courtly estates in medieval Europe, where a leisured class of nobles achieved status through hereditary ranking, competitive banquets, dazzling aesthetic displays, and the retention of household slaves captured in war. Remarkably, the coexistence of two such clearly opposed value systems among foragers inhabiting adjacent parts of the Pacific littoral has excited little interest in anthropologists, historians, or archaeologists to date. We consider the implications, which cast doubt on some key orthodoxies concerning the nature of culture areas, modes of subsistence, and political evolution. We argue that the political creativity of foraging peoples has been severely underrated. [hunter‐gatherers, slavery, schizmogenesis, culture areas, North America]

A cumulative hierarchy of sets for constructive set theory

The von Neumann hierarchy of sets is heavily used as a basic tool in classical set theory, being an underlying ingredient in many proofs and concepts. In constructive set theories like without the powerset axiom however, it loses much of its potency by ceasing to be a hierarchy of sets as its single stages become only classes. This article proposes an alternative cumulative hierarchy which does not have this drawback and provides examples of how it can be used to prove new theorems in .

‘I felt a noble shock’: James Boswell in German Princely Courts

The article deals with James Boswell’s (1740–1795) attitudes towards the courtly milieu in the context of eighteenth-century British court discourse. The central argument is that, strongly contrary to the anti-court ethos of his intellectual and social milieu, Boswell had an affirmative and enthusiastic attitude towards the court. Moreover, the fact that he was neither an Addisonian moralist ‘spectator’ nor a cynical court aristocrat like Lord Chesterfield, but in many senses a highly affective ‘man of feeling’ of the age, did not diminish the uniqueness of his positive view of court culture. On the one hand, Boswell’s appreciation of the court was connected with his firm monarchism and belief in hereditary rank; on the other hand, he was aesthetically fascinated by the splendour and magnificence of the courtly milieu. His appraisal of the court did not include the common-sense moralism of the moral weeklies or the cynical observations of the aristocratic court discourse; rather his attitude was immediate, emotional, and enthusiastic in the spirit of the cult of sensibility.

Relativized ordinal analysis: The case of Power Kripke–Platek set theory

The paper relativizes the method of ordinal analysis developed for Kripke–Platek set theory to theories which have the power set axiom. We show that it is possible to use this technique to extract information about Power Kripke–Platek set theory, KP(P).As an application it is shown that whenever KP(P)+AC proves a Π2P statement then it holds true in the segment Vτ of the von Neumann hierarchy, where τ stands for the Bachmann–Howard ordinal.

A nonperturbative solution of the nonlinear BBGKY hierarchy for marginal correlation operators

We consider the problem of the rigorous description of nonequilibrium quantum correlations. Within the framework of an alternative approach to the description of the evolution of states of finitely many particles in terms of correlation operators governed by the von Neumann hierarchy, we derive the nonlinear quantum Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) hierarchy for marginal correlation operators that is adopted to the description of quantum infinite‐particle systems as well. A nonperturbative solution of the Cauchy problem of the nonlinear quantum BBGKY hierarchy for marginal correlation operators is constructed. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Burial practices and social complexity: Jomon examples

Many archaeologists investigated the burial practices of the Jomon in order to clarify emerging social complexity, especially in the 1950s. Recently, since the social complexity of the Jomon became an important issue, burial practice has been recognised as an indicator of a hereditary ranking system. As I have noted elsewhere, there is no clear evidence that a hereditary ranking system existed in Jomon society. However, instead of searching for hereditary ranking in the Jomon, burial practices could be analysed from another aspect. The temporal and regional distribution of Jomon burial practices has been clarified. In the Kanto district, communal graves appeared in the early Late Jomon. This type of burial has been discovered only in this area. In the same period, some burial practices also appeared in other areas of Eastern Japan. Although this change from Middle to Late Jomon has been recognised, it has not been investigated from the perspective of social complexity. In this paper, I will try to examine the change in burial practices from the Middle to the Late Jomon in terms of social complexity.

Dynamics of correlations of Bose and Fermi particles

We discuss the origin of the microscopic description of correlations in quantum many-particle systems obeying Fermi–Dirac and Bose–Einstein statistics. For correlation operators that give the alternative description of the quantum state evolution of Bose and Fermi particles, we deduce the von Neumann hierarchy of nonlinear equations and construct the solution of its initial-value problem in the corresponding spaces of sequences of trace class operators. The links of constructed solution both with the solution of the quantum BBGKY hierarchy and with the nonlinear BBGKY hierarchy for marginal correlation operators are discussed. The solutions of the Cauchy problems of these hierarchies are constructed, in particular for initial data satisfying a chaos property. Copyright © 2010 John Wiley & Sons, Ltd.

Anglophilia: Deference, Devotion, and Antebellum America

‘No community’, observed New York lawyer and diarist George Templeton Strong on the eve of the American Civil War, ‘worships hereditary rank and station like a democracy’. As was usual with Strong, this comment was neither fully complimentary nor wholly condemnatory, but reflected his own mixed reaction to the visit of Albert Edward, Prince of Wales, to the United States in 1860, an analysis of which constitutes the opening chapter of this study of America's relationship with British culture in the construction of its own national identity in the antebellum era. This is no straightforward study of American reverence for the British monarchy, however, but rather a sophisticated analysis of the cultural semiotics of English élitism as revealed through art, literature and intellectualism in the antebellum republic. It is, in the author's words, ‘about absences and about the value of the symbolic forms and rituals that Americans excluded as they shaped their democratic culture in the years after independence from England … about paying respects to the symbolic value of England’ (p. xxiii). Informed by the work of, among others, Edward Shils, Tom Nairn, Michel de Certeau and Clifford Geertz, Elisa Tamarkin invites us not merely to rediscover a facet of nineteenth-century American culture which, as she notes, has not received the scholarly attention it merits, but proposes that it is within the lineaments of ‘Anglophilia’, broadly conceived, that Americans defined their ‘Americanness’. It is, in short, a study of American nationalism; how this was constructed and expressed across American culture—through its art, its rituals, its literature, and its universities—and an attempt to broaden, and deepen, our appreciation of ‘how nationalism, as a form of feeling, an ideology, and a set of practices, works every bit as seriously at bringing some aspects of the outside in, as it does at keeping others out’ (p. xxvi).

Evolution of correlations of quantum many-particle systems

We consider the origin of the microscopic description of correlations in quantumsystems. For correlation operators that give the alternative description ofthe quantum state evolution of many-particle systems, we deduce the vonNeumann hierarchy of nonlinear equations and discuss the relationships ofits solution both with the solution of the BBGKY hierarchy and with thes-particle correlation operators. A solution of the von Neumann hierarchy is constructed inthe form of an expansion over particle clusters whose evolution is described by thecorresponding order cumulant (semi-invariant) of evolution operators of the von Neumannequations for the density operators. For the initial data from the space of sequences of traceclass operators the existence of a strong and a weak solution of the Cauchy problem isproved.

And the sun pursued the moon: symbolic knowledge and traditional authority among the Makassar

Over the course of a thousand years, from 600 to 1600 CE, the Java Sea was dominated by a ring of maritime kingdoms whose rulers engaged in long-distance raiding, trading, and marriage alliances with one another. And the Sun Pursued the Moon explores the economic, political, and symbolic processes by which early Makassar communities were incorporated into this regional system. As successive empires like Srivijaya, Kediri, Majapahit, and Melaka gained hegemony over the region, they introduced different models of kingship in peripheral areas like the Makassar coast of South Sulawesi. As each successive model of royal power gained currency, it became embedded in local myth and ritual. By the time the kings of South Sulawesi converted to Islam at the beginning of the seventeenth century, at least six such models were present in the area. Islam introduced a whole new set of competing religious and political models, adding to the symbolic complexity of the area. To better understand the relationship between symbolic knowledge and traditional royal authority in Makassar society, Thomas Gibson draws on a wide range of sources and academic disciplines. He shows how myth and ritual link practical forms of knowledge (boat-building, navigation, agriculture, warfare) to basic social categories such as gender and hereditary rank, as well as to environmental, celestial, and cosmological phenomena. He also shows how concrete historical agents have used this symbolic infrastructure to advance their own political and ideological purposes. Gibson concludes by situating this material in relation to Islam and to life-cycle rituals.

Inaccessible set axioms may have little consistency strength

The paper investigates inaccessible set axioms and their consistency strength in constructive set theory. In ZFC inaccessible sets are of the form V κ where κ is a strongly inaccessible cardinal and V κ denotes the κth level of the von Neumann hierarchy. Inaccessible sets figure prominently in category theory as Grothendieck universes and are related to universes in type theory. The objective of this paper is to show that the consistency strength of inaccessible set axioms heavily depend on the context in which they are embedded. The context here will be the theory CZF − of constructive Zermelo–Fraenkel set theory but without ∈-Induction (foundation). Let INAC be the statement that for every set there is an inaccessible set containing it. CZF −+ INAC is a mathematically rich theory in which one can easily formalize Bishop style constructive mathematics and a great deal of category theory. CZF −+ INAC also has a realizability interpretation in type theory which gives its theorems a direct computational meaning. The main result presented here is that the proof theoretic ordinal of CZF −+ INAC is a small ordinal known as the Feferman–Schütte ordinal Γ 0 .

Logically Possible Machines

I use modal logic and transfinite set-theory to define metaphysical foundations for a general theory of computation. A possible universe is a certain kind of situation; a situation is a set of facts. An algorithm is a certain kind of inductively defined property. A machine is a series of situations that instantiates an algorithm in a certain way. There are finite as well as transfinite algorithms and machines of any degree of complexity (e.g., Turing and super-Turing machines and more). There are physically and metaphysically possible machines. There is an iterative hierarchy of logically possible machines in the iterative hierarchy of sets. Some algorithms are such that machines that instantiate them are minds. So there is an iterative hierarchy of finitely and transfinitely complex minds.

Duals for Non-Abelian Lattice Gauge Theories by Categorical Methods

We introduce duals for non-Abelian lattice gauge theories in dimension at least three by using a categorical approach to the notion of duality in lattice theories. We first discuss the general concepts for the case of a dual-triangular lattice (i.e., the dual lattice is triangular) and find that the commutative tetrahedron condition of category theory can directly be used to define a gauge-invariant action for the dual theory. We then consider the cubic lattice (where the dual is cubic again). The case of the gauge group SU(2) is discussed in detail. We will find that in this case gauge connections of the dual theory correspond to SU(2) spin networks, suggesting that the dual is a discrete version of a quantum field theory of quantum simplicial complexes (i.e. the dual theory lives already on a quantized level in its classical form). We conclude by showing that our notion of duality leads to a hierarchy of extended lattice gauge theories closely resembling the one of extended topological quantum field theories. The appearance of this hierarchy can be understood by the quantum von Neumann hierarchy introduced by one of the authors in previous work.

Toward quantum mathematics. I. From quantum set theory to universal quantum mechanics

We develop the old idea of von Neumann of a set theory with an internal quantum logic in a modern categorical guise [i.e., taking the objects of the category H of (pre-)Hilbert spaces and linear maps as the sets of the basic level]. We will see that in this way it is possible to clarify the relationship between categorification and quantization and besides this to understand that in some sense a categorificational approach to quantization is a discretized version of the one taken by noncommutative geometry. The tower of higher categorifications will appear as the analog of the von Neumann hierarchy of classical set theory (where by classical set theory, we will understand the usual Zermelo–Fraenkel system). Finally, we make a suggestion of how to understand all the different categorifications as different realizations of one and the same abstract structure by viewing quantum mechanics as universal in the sense of category theory. This gives the possibility to view extended topological quantum field theories purely as involving an abstract notion of quantum mechanics plus representation theory without the need to enlarge the class of kinematic structures of quantum systems on each step of categorification. In a future part of the work we will apply the language developed here to deal especially with the question of a categorification of the manifold notion.

Objects of Memory: The Ethnography and Archaeology of Heirlooms

With the emergence of chiefdoms, a new ideology of inherited social difference had to be created and sustained over time. One way that inherited social inequalities may have been constructed, legitimated, and maintained is through the transmission of heirlooms or artifacts that objectified a collective ancestral past. Archaeologists have generally viewed heirlooms as anomalies or complications in the archaeological record. In this paper, however, I argue that, if identified, heirlooms have the potential to provide a richer and finer-grained understanding of the human past, in general, and to aid in the determination of hereditary rank, in particular. I discuss and compare the ethnographic evidence for heirloom use in bands, tribes, and chiefdoms, and, based on this evidence, I suggest criteria by which heirlooms might be identified in the archaeological record. Some examples of possible heirlooms from the archaeological literature are also presented. Finally, an evolutionary model for the circulation and disposal of heirlooms is proposed.

Inner Models and Large Cardinals

In this paper, we sketch the development of two important themes of modern set theory, both of which can be regarded as growing out of work of Kurt Gödel. We begin with a review of some basic concepts and conventions of set theory. §0. The ordinal numbers were Georg Cantor's deepest contribution to mathematics. After the natural numbers 0, 1, …, n, … comes the first infinite ordinal number ω, followed by ω + 1, ω + 2, …, ω + ω, … and so forth. ω is the first limit ordinal as it is neither 0 nor a successor ordinal. We follow the von Neumann convention, according to which each ordinal number α is identified with the set {ν ∣ ν α} of its predecessors. The ∈ relation on ordinals thus coincides with &lt;. We have 0 = ∅ and α + 1 = α ∪ {α}. According to the usual set-theoretic conventions, ω is identified with the first infinite cardinal ℵ0, similarly for the first uncountable ordinal number ω1 and the first uncountable cardinal number ℵ1, etc. We thus arrive at the following picture: The von Neumann hierarchy divides the class V of all sets into a hierarchy of sets Vα indexed by the ordinal numbers. The recursive definition reads: (where } is the power set of x); Vλ = ∪v&lt;λVv for limit ordinals λ. We can represent this hierarchy by the following picture.

A classification of an iterative hierarchy

A classification of an iterative hierarchy