A class of metric theories of gravitation on Minkowski spacetime is considered, which is—provided that certain assumptions (staying close to the original ideas of Einstein) are made—the almost most general one that can be considered. In addition to the Minkowskian metric G a dynamical metric H (called the Einstein metric)is defined by means of a second-rank tensor field S (referred to as gravitational potential).The theory is defined by a Lagrangian ℒ, from which the field equations as well as, e.g., (...) the energy-momentum tensor field for the gravitational field follow. The case of weak fields is considered explicitly. The static, spherically and time-inversal symmetric field is calculated, and as a first step to investigate the theory's viability the parameters are fitted to the experimental data of the perihelion advance and the deflection of light at the Sun. Finally the question of gauge freedoms in the gravitational potential is briefly discussed. (shrink)

The present paper is a sequel to Robles et al. :349–374, 2020. https://doi.org/10.1007/s10849-019-09306-2). A class of implicative expansions of Kleene’s 3-valued logic functionally including Łukasiewicz’s logic Ł3 is defined. Several properties of this class and/or some of its subclasses are investigated. Properties contemplated include functional completeness for the 3-element set of truth-values, presence of natural conditionals, variable-sharing property and vsp-related properties.

We define a class of higher inductive types that can be constructed in the category of sets under the assumptions of Zermelo‐Fraenkel set theory without the axiom of choice or the existence of uncountable regular cardinals. This class includes the example of unordered trees of any arity.

GEORGE BOOLE died one hundred years ago. This essay from Cork is intended as commemorative of a great man, for too long forgotten in the College he served so well.

In this paper the familiar construction of the category of coalgebras for a cartesian comonad is extended to the setting of “algebraic set theory”. In particular, it is shown that, under suitable assumptions, several kinds of categories of classes are stable under the formation of coalgebras for a cartesian comonad, internal presheaves and comma categories.

Since the onset of the latest United States (U.S.) recession (beginning in December 2007), the U.S. economy has been posting high unemployment levels consistently exceeding 8 percent. Of specific interest, the U.S. Department of Labor, Bureau of Labor Statistics (BLS), reports on a specific subset of the U.S. unemployed: the long‐term unemployed, defined as those who are unemployed for 27 weeks and over. Since December 2009, the share of the long‐term unemployed of the total U.S. unemployed has exceeded 40 percent (...) (through April 2012), the highest level since 1948 when data was first collected. A phenomenon of this recession is an alleged public bias by American private sector employers against hiring the long‐term unemployed, or even simply those unemployed. While the authors support the removal of discrimination against the unemployed in job advertisements, they cannot support the larger notion of including those who are unemployed as a protected class of employees. Becoming or being unemployed is a state that one can change, and based on the lack of research on how widespread this discrimination is (beyond anecdotal stories or limited research surveys), they believe that extending protection under equal employment opportunity legislation would be overreaching and inappropriate at this time. (shrink)

A transnational capitalist class has emerged as that segment of the world bourgeoisie that represents transnational capital, the owners of the leading worldwide means of production as embodied in the transnational corporations and private financial institutions. The spread of TNCs, the sharp increase in foreign direct investment, the proliferation of mergers and acquisitions across national borders, the rise of a global financial system, and the increased interlocking of positions within the global corporate structure, are some empirical indicators of the (...) transnational integration of capitalists. The TCC manages global rather than national circuits of accumulation. This gives it an objective class existence and identity spatially and politically in the global system above any local territories and polities. The TCC became politicized from the 1970s into the 1990s and has pursued a class project of capitalist globalization institutionalized in an emergent transnational state apparatus and in a "Third Way" political program. The emergent global capitalist historic bloc is divided over strategic issues of class rule and how to achieve regulatory order in the global economy. Contradictions within the ruling bloc open up new opportunities for emancipatory projects from global labor. (shrink)

A mistake which occurred in the derivation of the field equations from the Lagrangian is corrected. Unfortunately many of the expressions given in the article have to be changed, although the results do not change qualitatively, but only quantitatively.

This paper investigates a distributed coordination control for a class of high-order uncertain multiagent systems. Under the framework of iterative learning control, a novel fully distributed learning protocol is devised for the coordination problem of MASs including time-varying parameter uncertainties as well as actuator saturations. Meanwhile, the learning updating laws of various parameters are proposed. Utilizing Lyapunov theory and combining with Graph theory, the proposed algorithm can make each follower track a leader completely over a limited time interval even (...) though each follower is without knowing the dynamics of the leader. Moreover, the extension to formation control is made. The validity and feasibility of the algorithm are verified conclusively by two examples. (shrink)

Ventricular Fibrillation is responsible for a majority of sudden cardiac death, but little is known about how ventricular tachycardia (VT) degenerates into ventricular fibrillation. Several clinical studies focused only on preventing VT with a class III antiarrhythmic drug resulted in many deaths. Our simulations investigate the interactions between an antiarrhythmic drug likely to suppress a VT and a Figure 8 reentry. A parameter AAR is introduced to increase the action potential duration and therefore simulate various Class III drugs. (...) Simulations are ran under several conditions (phases of the reentry, values of AAR, durations). They show that a VT can be suppressed whatever the phase of the reentry but it strongly depends on the duration of the effect. It confirms that a drug which can suppress a reentry can also worsen it. It also shows a great variety of activation patterns and thus the complexity of antiarrhythmic drugs effects. Simulations also demonstrate that suppressing VT is an increasing function of AAR. (shrink)

LetMbe a countably infinite ω-categorical structure. Consider Aut(M) as a complete metric space by definingd(g, h) = Ω{2−n:g(xn) ≠h(xn) org−1(xn) ≠h−1(xn)} where {xn:n∈ ω} is an enumeration ofMAn automorphism α ∈ Aut(M) is generic if its conjugacy class is comeagre. J. Truss has shown in [11] that if the set P of all finite partial isomorphisms contains a co-final subset P1closed under conjugacy and having the amalgamation property and the joint embedding property then there is a generic automorphism. In (...) the present paper we give a weaker condition of this kind which is equivalent to the existence of generic automorphisms. Really we give more: a characterization of the existence of generic expansions (defined in an appropriate way) of an ω-categorical structure. We also show that Truss' condition guarantees the existence of a countable structure consisting of automorphisms ofMwhich can be considered as an atomic model of some theory naturally associated toM. We do it in a general context of weak models for second-order quantifiers.The author thanks Ludomir Newelski for pointing out a mistake in the first version of Theorem 1.2 and for interesting discussions. Also, the author is grateful to the referee for very helpful remarks. (shrink)

In Dirac-Bergmann constrained dynamics, a first-class constraint typically does not _alone_ generate a gauge transformation. By direct calculation it is found that each first-class constraint in Maxwell's theory generates a change in the electric field E by an arbitrary gradient, spoiling Gauss's law. The secondary first-class constraint p^i,_i=0 still holds, but being a function of derivatives of momenta, it is not directly about E. Only a special combination of the two first-class constraints, the Anderson-Bergmann -Castellani gauge (...) generator G, leaves E unchanged. This problem is avoided if one uses a first-class constraint as the generator of a _canonical transformation_; but that partly strips the canonical coordinates of physical meaning as electromagnetic potentials and makes the electric field depend on the smearing function, bad behavior illustrating the wisdom of the Anderson-Bergmann Lagrangian orientation of interesting canonical transformations. The need to keep gauge-invariant the relation dot{q}- dH/dp= -E_i -p^i=0 supports using the primary Hamiltonian rather than the extended Hamiltonian. The results extend the Lagrangian-oriented reforms of Castellani, Sugano, Pons, Salisbury, Shepley, _etc._ by showing the inequivalence of the extended Hamiltonian to the primary Hamiltonian even for _observables_, properly construed in the sense implying empirical equivalence. Dirac and others have noticed the arbitrary velocities multiplying the primary constraints outside the canonical Hamiltonian while apparently overlooking the corresponding arbitrary coordinates multiplying the secondary constraints _inside_ the canonical Hamiltonian, and so wrongly ascribed the gauge quality to the primaries alone, not the primary-secondary team G. Hence the Dirac conjecture about secondary first-class constraints rests upon a false presupposition. The usual concept of Dirac observables should also be modified to employ the gauge generator G, not the first-class constraints separately, so that the Hamiltonian observables become equivalent to the Lagrangian ones such as the electromagnetic field F. (shrink)

In our paper “A general characterization of the variable-sharing property by means of logical matrices”, a general class of so-called “Relevant logical matrices”, RMLs, is defined. The aim of this paper is to define a class of simpler Relevant logical matrices RMLs′serving the same purpose that RMLs, to wit: any logic verified by an RML′has the variable-sharing property and related properties predicable of the logic of entailment E and of the logic of relevance R.

ABSTRACTAnxiety and depression diagnoses are associated with suicidal thoughts and behaviours. However, a categorical understanding of these associations limits insight into identifying dimensional mechanisms of suicide risk. This study investigated anxious and depressive features through a lens of suicide risk, independent of diagnosis. Latent class analysis of 97 depression, anxiety, and suicidality-related items among 616 psychiatric outpatients indicated a 3-class solution, specifically: a higher suicide-risk class uniquely differentiated from both other classes by high reported levels of depression (...) and anxious arousal; a lower suicide-risk class that reported levels of anxiety sensitivity and generalised worry comparable to Class 1, but lower levels of depression and anxious arousal; and a low to non-suicidal class that reported relatively low levels across all depression and anxiety measures. Discriminants of the higher suicide-risk class included borderline personality disorder; report... (shrink)

In the complex environment, the suddenly changing structural parameters and abrupt actuator failures are often encountered, and the negligence or unproper handling method may induce undesired or unacceptable results. In this paper, taking the suddenly changing structural parameters and abrupt actuator failures into consideration, we focus on the robust adaptive control design for a class of heterogeneous Takagi–Sugeno fuzzy nonlinear systems subjected to discontinuous multiple uncertainties. The key point is that the switch modes not only vary with the system (...) time but also vary with the system states, and the intrinsic heterogeneous characteristics make it difficult to design stable controllers. Firstly, the concepts of differential inclusion are introduced to describe the heterogeneous fuzzy systems. Meanwhile, a fundamental lemma is provided to demonstrate the criteria of the boundness for a Filippov solution. Then, by using the set-valued Lie derivative of the Lyapunov function and introducing a vector of specific continuous functions, the closed-loop T-S fuzzy differential inclusion systems are proved to be ultimately bounded. The sufficient conditions for system stability are derived in term of linear matrix inequalities, which can be solved directly. Finally, a numerical example is provided to illustrate the effectiveness of the proposed control algorithm. (shrink)

Most human societies exhibit a distinct class structure, with an elite, middle classes, and a bottom class, whereas animals form simple dominance hierarchies in which individuals with higher fighting ability do not appear to form coalitions to “oppress” weaker individuals. Here, we extend our model of primate coalitions and find that a division into a bottom class and an upper class is inevitable whenever fitness-enhancing resources, such as food or real estate, are exploitable or tradable and (...) the members of the bottom class cannot easily leave the group. The model predicts that the bottom class has a near flat, low payoff and always comprises at least half the society. The upper class may subdivide into one or more middle class(es), resulting in improved payoff for the topmost members (elite). The model predicts that the bottom class on its own is incapable of mounting effective counter-coalitions against the upper class, except when receiving support from dissatisfied members of the middle class(es). Such counter-coalitions can be prevented by keeping the payoff to the lowest-ranked members of the middle classes (through concessions) well above that of the bottom class. This simple model explains why classes are also absent in nomadic hunter-gatherers and predominate in (though are not limited to) societies that produce and store food. Its results also agree well with various other known features of societies with classes. (shrink)

Most discussions on animal experimentation refer to domesticated animals and regulations are tailored to this class of animals. However, wild animals are also used for research, e.g., in biological field research that is often directed to fundamental ecological-evolutionary questions or to conservation goals. There are several differences between domesticated and wild animals that are relevant for evaluation of the acceptability of animal experiments. Biological features of wild animals are often more critical as compared with domesticated animals because of their (...) survival effects. An important issue is what is called here ``natural suffering'''': the suffering from natural circumstances. Should this type of suffering be taken into account when suffering from experimentation is evaluated? As an answer, it is suggested that ``natural functioning'''' should be considered as an additional standard in the evaluation of wild animal experimentation. Finally, two topics related to the ecological context are considered. Firstly, the often inevitable involvement of non-research animals in wild animal experimentation, and secondly, the eco-centric approach to nature conservation. According to the latter position, animals are subordinated to ecosystems. All these aspects make the evaluation of wild animal experiments much more complex than experiments with domesticated animals. Preliminary scores are proposed to deal with these aspects. It is argued that this should not lead to a more complex governmental regulation, since an effective maintenance and control are hard to realize and one may loose the cooperation of researchers themselves. In addition, non-governmental professional organizations such as research societies and funding organizations play a pivotal role. (shrink)

Materialismo dialético, luta de classes e insights filosóficos sobre a educação a partir de Slavoj Žižek Resumo: O artigo aborda a concepção de luta de classes no atual cenário histórico, político e social. O dogma das democracias ocidentais sugere que vivemos numa era pós-ideológica. Isso implica que não há mais espaço para a ideia de luta de classes. Contudo, segundo Žižek, é esse discurso que deve ser enquadrado no campo ideológico. Žižek retoma o conceito de materialismo dialético a fim de (...) demonstrar a contradição interna ao campo ideológico de nossa sociedade dita pós-ideológica. Nesse momento, o conceito de luta de classes retorna à cena. A luta de classes não consiste num antagonismo entre dois polos num espaço comum, mas na fissura inerente ao próprio espaço. Para desenvolver o tema, cabe, antes, abordar o conceito de materialismo teológico de Walter Benjamin, que fundamenta, substancialmente, o conceito de materialismo dialético de Žižek. Importante, igualmente, retomar uma reflexão sobre o conceito de pulsão de morte em Freud, já que tal conceito exprime exatamente a fissura interna à realidade que condiciona a luta de classes. Convém, ademais, compreender como a ideia de educação pode ser pensada a partir da contradição que mobiliza a luta de classes.Palavras-chaves: Materialismo dialético. Luta de classes. Ideologia. Educação. Dialetic materialism, class struggle and philosophical insights on education from Slavoj Žižek: The article discusses the concept of class struggle in the current historical, political and social scenario. The dogma of Western democracies suggests that we live in a post-ideological era. This implies that there is no longer any room for the idea of ​​class struggle. However, according to Žižek, it is this discourse that must be framed in the ideological domain. Žižek takes up the concept of dialectical materialism in order to demonstrate the internal contradiction to the ideological field of our so-called post-ideological society. At this point, the concept of class struggle returns to the scene. The class struggle does not consist of an antagonism between two poles in a common space, but in the fissure inherent in the space itself. To develop the theme, it is first necessary to approach Walter Benjamin's concept of theological materialism, which substantially supports Žižek's concept of dialectical materialism. It is also important to resume a reflection on the concept of the death instinct in Freud, because this concept expresses exactly the internal fissure in reality which conditions the class struggle. In addition, it is important to understand how the idea of ​​education can be thought of from the contradiction that mobilizes the class struggle.Keywords: Dialectical materialism. Class struggle. Ideology. Education. Matérialisme dialetique, lutte de classe et insights philosophiques sur l'éducation de Slavoj Zižek Résumé: L'article aborde le concept de lutte des classes dans le scénario historique, politique et social actuel. Le dogme des démocraties Occidentales sugère que nous vivons à une époque post-idéologique. Cela implique qu'il n'y a plus de place pour l'idée de lutte de classe. Cependant, selon Žižek, c'est ce discours qui doit être cadré dans le domaine idéologique. Žižek reprend le concept de matérialisme dialectique afin de démontrer la contradiction interne au champ idéologique de notre soi-disant société post-idéologique. À ce moment, le concept de lutte des classes revient sur la scène. La lutte des classes ne consiste pas en un antagonisme entre deux pôles dans un espace commun, mais dans la fissure inhérente à l'espace lui-même. Pour développer le thème, il est d'abord nécessaire d'approcher le concept de matérialisme théologique de Walter Benjamin, qui étaye substantiellement le concept de matérialisme dialectique de Žižek. Il est également important de reprendre une réflexion sur le concept d'instinct de mort chez Freud, car ce concept exprime exactement la fissure interne à la réalité qui conditionne la lutte des classes. En outre, il est important de comprendre comment l'idée de l'éducation peut être pensée à partir de la contradiction qui mobilise la lutte des classes.Mots-clés: Matérialisme dialectique. Lutte des classes. Idéologie. Éducation. Data de registro: 09/02/2020Data de aceite: 28/08/2020. (shrink)

A new reduction class is presented for the satisfiability problem for well-formed formulas of the first-order predicate calculus. The members of this class are closed prenex formulas of the form ∀ x∀ yC. The matrix C is in conjunctive normal form and has no disjuncts with more than three literals, in fact all but one conjunct is unary. Furthermore C contains but one predicate symbol, that being unary, and one function symbol which symbol is binary.

We study various classes of maximality principles, \\), introduced by Hamkins :527–550, 2003), where \ defines a class of forcing posets and \ is an infinite cardinal. We explore the consistency strength and the relationship of \\) with various forcing axioms when \. In particular, we give a characterization of bounded forcing axioms for a class of forcings \ in terms of maximality principles MP\\) for \ formulas. A significant part of the paper is devoted to studying the (...) principle MP\\) where \ and \ defines the class of stationary set preserving forcings. We show that MP\\) has high consistency strength; on the other hand, if \ defines the class of proper forcings or semi-proper forcings, then by Hamkins, MP\\) is consistent relative to \. (shrink)

Given a class of linear order types C, we identify and study several different classes of trees, naturally associated with C in terms of how the paths in those trees are related to the order types belonging to C. We investigate and completely determine the set-theoretic relationships between these classes of trees and between their corresponding first-order theories. We then obtain some general results about the axiomatization of the first-order theories of some of these classes of trees in terms (...) of the first-order theory of the generating class C, and indicate the problems obstructing such general results for the other classes. These problems arise from the possible existence of nondefinable paths in trees, that need not satisfy the first-order theory of C, so we have started analysing first order definable and undefinable paths in trees. (shrink)

Small non‐coding RNAs (microRNAs or miRs) represent one of the most fertile areas of cancer research and recent advances in the field have prompted us to reconsider the traditional concept of cancer. Some miRs exert negative control over the expression of numerous oncoproteins in normal cells and consequently their deregulation is believed to be an important mechanism underlying cancer development and progression. Owing to their distinct patterns of expression associated with cancer type, remarkable stability and presence in blood and other (...) body fluids, miRs are considered to be highly promising cancer biomarkers. The identification of “miR signatures” associating cancer cell phenotypes with disease outcome and specific risk factor exposures will undoubtedly open new avenues for early diagnosis and therapy of cancer, as well as for the development of novel strategies for cancer prevention. (shrink)

We define a class of so-called ∑-sets as a natural closure of recursively enumerable sets Wn under the relation “∈” and study its properties.

Reaction-diffusion systems which have reaction term satisfying f(-q) = -f(q) tend strongly to form striped patterns. Haken’s slaving principle is used to derive differential equations for unstable mode amplitudes close to the Turing instability. This connects a dynamical symmetry to pattern selection, with possible relevance to biological and chemical pattern-forming phenomena.

A necessary condition for the development of a philosophical culture is the possession of a history of philosophy that conserves the experience of posing and discussing philosophical problems. Apologetics, dogmatism, a rigid devotion to the class approach, and ignoring universal human values for a long time dominated our social science and substantially deformed the way the history of philosophy was taught, giving rise to a number of stereotypes that hinder the revival of the skills of a culture of professional (...) philosophizing. The purpose of the present article is to draw the attention of philosophers to the problem of presenting material on the history of philosophy in a philosophy course. (shrink)

The CMI Millennium “P vs NP Problem” can be resolved e.g. if one shows at least one counterexample to the "P = NP" conjecture. A certain class of problems being such counterexamples will be formulated. This implies the rejection of the hypothesis that "P = NP" for any conditions satisfying the formulation of the problem. Thus, the solution "P is different from NP" of the problem in general is proved. The class of counterexamples can be interpreted as any (...) quantum superposition of any finite set of quantum states. The Kochen-Specker theorem is involved. Any fundamentally random choice among a finite set of alternatives belong to "NP" but not to "P". The conjecture that the set complement of "P" to "NP" can be described by that kind of choice exhaustively is formulated. (shrink)

We compare several closely related continuum invariants, i.e., $\mathfrak{a}$, $\mathfrak{a}_\mathfrak{e}$, $\mathfrak{a}_\mathfrak{p}$ in two forcing models. And we shall ask some open questions in this field.

The Dirac field and its quanta are obtained from the imposition of an infinite member of Dirac 2 nd class constraints on a system of complex scalar fields having an indefinite internal metric. The spin-1/2 character of the constrained system follows from constraint-induced coupling of the scalar system's independent internal and space-time symmetries, from constraint restrictions on allowed symmetries. The resulting spinor field quanta are seen to exist as a class of “elementary excitations” belonging to a dynamical algebra (...) existing naturally within the system of complex scalar fields. (shrink)

The logic E4 is related to Brady’s BN4 in a similar way to which Anderson and Belnap’s logic of entailment E is related to their logic of the relevant implication R. In ‘A companion to Brady’s 4-valued relevant logic: the 4-valued logic of entailment E4’, quoted in this paper, three alternatives to BN4 and another three to E4 are summarily introduced in a couple of pages as the only alternatives containing Routley and Meyer’s basic logic B, provided some conditions are (...) fulfilled. The aim of this note is to prove BN4 and its three alternatives are the same logic up to some point, since they are functionally equivalent to each other, as it is the case with E4 and its three alternatives, which are also functionally equivalent to each other; to some extent, E4 is superior to BN4, since the latter is functionally included in the former, but not conversely. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:A Place for Healing:A Hospital Art Class, Writing, and a Researcher's TaskJulia Kellman (bio)Introduction[O]bjects transform the top of our chest into a site of memory. I think of private landscapes like this one as querencias, places that hold the heart. The word has been translated as homing instinct and affection. Expatriate Alastair Reid introduced me to it in 1965, writing about the Spanish bullfight in The New Yorker. (...) After the first wound the bull chooses his querencia, the place in the ring where he returns for a moment to rest before the fight goes on, and where he finally dies. Querencia comes from the common Spanish verb querer; among its many meanings are to love, to want, to hold, and to command. Reid spoke of hometowns and native countries as querencias; exiles cling to their memories of them.1Place, "space that has the capacity to be remembered and to evoke what is most precious,"2 by its nature orients us to a particular perspective, to a way of looking at the world. Each place has its own local accent, its own constellation of habits, its own rhythm of language and thought. We are grounded in landscape in the same manner that we are situated in our social world, imprinted like other creatures on a typography, pattern of weather, cycle of seasons, scents, and colors.3Our hearts, too, are embedded in such places; and in this article, through this "act of personal witness," this "inscription of a self and a description of an object" as the anthropologist and writer Ruth Benhar4 describes it, we will see how the members of an art class for people with HIV/AIDS at a local hospital have similarly become grounded in their art space and in the tiny art community that has grown up around it. Additionally, we will discover the importance of a more descriptive style of writing as means for examining the role of art in the lives of people who are ill, for their various difficult [End Page 106] situations call for particular clarity and empathy that both honors and relates the stories of their lives. It will become clear as this article proceeds that the personal engagement of a researcher/writer in such a situation is critical as well. For not only must she be open—vulnerable, as Behar suggests—to the people with whom she works as a means of spanning the chasm between a life of illness and a life of health, but she must also be sensitive to the reader's needs, for she is the reader's guide and surrogate.5 This role as guide and alter-ego demands that the researcher tell the story of other lives in a manner that enables the reader to empathetically and eagerly undertake a journey with the researcher into a world unlike her own.6Personal Engagement: The Researcher/WriterHoward Brody, doctor and medical ethicist, explains the necessity for stories of illness to be descriptive.7 He asserts that the stories in which we are most interested are not merely factual recitations; they are about what the illness means to the individual—they include how that person understands events. "It is far too simple-minded" he writes, to assume that "the writer of literature presents to us a world of fantasy that never existed whereas the author of a nonfictional pathography has some special insight into the world as it really exists, even if the relevant world is nothing but his own subjective experiences."8 He concludes "in stories of that sort (stories of the meaning of things) the line between so-called truth and fiction becomes more blurred and ceases to affect the uses we make of the stories for the deeper understanding of the human response to illness."9 Further, Brody continues, one must understand stories of sickness in order to truly develop a philosophical understanding of what it means to be ill. Such an understanding, Brody suggests, not only provides ethical guidance for health care workers and others but also will lead to improved care for patients and better education of health professionals.10 This view of... (shrink)

Let $\mathfrak{U}$ be an admissible structure. A $\mathrm{cPC}_d(\mathfrak{U})$ class is the class of all models of a sentence of the form $\neg\exists\bar{K} \bigwedge \Phi$, where $\bar{K}$ is an $\mathfrak{U}$-r.e. set of relation symbols and $\phi$ is an $\mathfrak{U}$-r.e. set of formulas of $\mathscr{L}_{\infty\omega}$ that are in $\mathfrak{U}$. The main theorem is a generalization of the following: Let $\mathfrak{U}$ be a pure countable resolvable admissible structure such that $\mathfrak{U}$ is not $\Sigma$-elementarily embedded in $\mathrm{HYP}(\mathfrak{U})$. Then a class $\mathbf{K}$ (...) of countable structures whose universes are sets of urelements is a $\mathrm{cPC}_d(\mathfrak{U})$ class if and only if for some $\Sigma$ formula $\sigma$ (with parameters from $\mathfrak{U}$), $\mathfrak{M}$ is in $\mathbf{K}$ if and only if $\mathfrak{M}$ is a countable structure with universe a set of urelements and $(\mathrm{HYP}_\mathfrak{U}(\mathfrak{M}), \mathfrak{U}, \mathfrak{M}) \models \sigma$, where $\mathrm{HYP}_\mathfrak{U}(\mathfrak{M})$, the smallest admissible set above $\mathfrak{M}$ relative to $\mathfrak{U}$, is a generalization of $\mathrm{HYP}$ to structures with similarity type $\Sigma$ over $\mathfrak{U}$ that is defined in this article. Here we just note that when $\mathrm{L}_\alpha$ is admissible, $\mathrm{HYP}_{\mathrm{L}\alpha}(\mathfrak{M})$ is $\mathrm{L}_\beta(\mathfrak{M})$ for the least $\beta \geq \alpha$ such that $\mathrm{L}_\beta(\mathfrak{M})$ is admissible, and so, in particular, that $\mathrm{HYP}_{\mathbb{HF}}(\mathfrak{M})$ is just $\mathrm{HYP}(\mathfrak{M})$ in the usual sense when $\mathfrak{M}$ has a finite similarity type. The definition of $\mathrm{HYP}_\mathfrak{U}(\mathfrak{M})$ is most naturally formulated using Adamson's notion of a +-admissible structure (1978). We prove a generalization from admissible to +-admissible structures of the well-known truncation lemma. That generalization is a key theorem applied in the proof of the generalized Spector-Gandy theorem. (shrink)