We prove an Omitting Types Theorem for certain algebraizable extensions of first order logic without equality studied in [SAI 00] and [SAY 04]. This is done by proving a representation theorem preserving given countable sets of infinite meets for certain reducts of ?- dimensional polyadic algebras, the so-called G polyadic algebras (Theorem 5). Here G is a special subsemigroup of (?, ? o) that specifies the signature of the algebras in question. We state and prove an independence result connecting our (...) representation theorem to Martin's axiom (Theorem 6). Also we show that the countable atomic G polyadic algebras are completely representable (Corollary 16) contrasting results on cylindric algebras. Several related results are surveyed. (shrink)

As climate change continues to be a pressing issue affecting businesses, firms are taking proactive measures by integrating carbon considerations into their overall strategic planning for environmental sustainability. Nonetheless, the question of whether it pays to be green remains inconclusively answered. Based on an analysis of the 200 largest public listed firms by market capitalisation in Malaysia, the findings indicated that most of the firms are still reactive in managing their carbon activities; however, corporate carbon strategy does, indeed, lead to (...) better financial performance. The findings reaffirmed that going green pays off, particularly for firms with higher levels of foreign ownership. Interestingly, an inverse relationship was observed among firms with higher levels of government shareholdings. Additionally, the firms have been categorised into six different groups based on their scope and level of corporate carbon strategies, ranging from “wait-and-see” to “all-round explorer” classifications. Taken together, these findings enrich corporate carbon and sustainability literature and offer insights into theoretical and policy implications, along with suggestions for future research. (shrink)

An interpolation Theorem is proved for first order logic with infinitary predicates. Our proof is algebraic via cylindric algebras.1.

Recital 33 GDPR has often been interpreted as referring to ‘broad consent’. This version of informed consent was intended to allow data subjects to provide their consent for certain areas of research, or parts of research projects, conditional to the research being in line with ‘recognised ethical standards’. In this article, we argue that broad consent is applicable in the emerging field of Computational Social Science (CSS), which lies at the intersection of data science and social science. However, the lack (...) of recognised ethical standards specific to CSS poses a practical barrier to the use of broad consent in this field and other fields that lack recognised ethical standards. Upon examining existing research ethics standards in social science and data science, we argue that they are insufficient for CSS. We further contend that the fragmentation of European Union (EU) law and research ethics sources makes it challenging to establish universally recognised ethical standards for scientific research. As a result, CSS researchers and other researchers in emerging fields that lack recognised ethical standards are left without sufficient guidance on the use of broad consent as provided for in the GDPR. We conclude that responsible EU bodies should provide additional guidance to facilitate the use of broad consent in CSS research. (shrink)

Technological advances in the field of medicine and health sciences not only manipulate the normal human body and sex but also provide for surgical and hormonal management of hermaphroditism. Consequently, sex assignment surgery has not only become a standard care for babies born with genital abnormalities in the West but even in some Muslim states. On the positive side, it goes a long way in saving children born with abnormal genitalia from numerous legal interdictions of the pre-sex corrective surgery. Nevertheless, (...) the larger ethical and legal questions that medical management of genital abnormality raises to some extent have not been adequately appreciated by contemporary Muslim responses. This article, therefore, in principle argues against surgical management of intersexuality during early infancy from the Islamic legal perspective. (shrink)

Both in church and culture, discussion of sexual orientation has far outpaced discussion of gender identity, leaving the churches with limited resources to respond to “bathroom bills” or to walk faithfully with transgender persons in their midst. This paper draws on the work of Rowan Williams and Sarah Coakley to argue for understanding gender transition as an eschatological formation ordered to the body’s grace. In critical conversation with Oliver O’Donovan, John Milbank, and David Cloutier, the paper offers a constructive, non-voluntarist (...) theological proposal for transgender affirmation in the service of participation in the triune life that exceeds gender. (shrink)

Fix a finite ordinal \ and let \ be an arbitrary ordinal. Let \ denote the class of cylindric algebras of dimension \ and \ denote the class of relation algebras. Let \\) stand for the class of polyadic algebras of dimension \. We reprove that the class \ of completely representable \s, and the class \ of completely representable \s are not elementary, a result of Hirsch and Hodkinson. We extend this result to any variety \ between polyadic algebras (...) of dimension \ and diagonal free \s. We show that that the class of completely and strongly representable algebras in \ is not elementary either, reproving a result of Bulian and Hodkinson. For relation algebras, we can and will, go further. We show the class \ is not closed under \. In contrast, we show that given \, and an atomic \, then for any \, \ is a completely representable \. We show that for any \, the class of completely representable algebras in certain reducts of \s, that happen to be varieties, is elementary. We show that for \, the the class of polyadic-cylindric algebras dimension \, introduced by Ferenczi, the completely representable algebras coincide with the atomic ones. In the last algebras cylindrifications commute only one way, in a sense weaker than full fledged commutativity of cylindrifications enjoyed by classical cylindric and polyadic algebras. Finally, we address closure under Dedekind-MacNeille completions for cylindric-like algebras of dimension \ and \s for \ an infinite ordinal, proving negative results for the first and positive ones for the second. (shrink)

We generalize two classical results on cylindric algebra to certain expansions of cylindric algebras where the extra operations are defined via first order formulas. The first result is the Neat Embedding Theorem of Henkin and the second is Monk's classical non-finitizability result of the class of representable algebras. As a corollary we obtain known classical results of Johnson and Biro published in the Journal of Symbolic logic.

We review, and in the process unify two techniques , for proving results concerning amalgamation in several classes studied in algebraic logic. The logical counterpart of these results adress interpolation and definability properties in modal and algebraic logic. Presenting them in a functorial context as adjoint situations, we show that both techniques can indeed be seen as instances of the use of the Keisler-Shelah ultrapower Theorem in proving Robinson's Joint Consistency Theorem. Some new results are surveyed. The results of this (...) paper are presented in such a way that further establishes the hitherto existing well developed duality theory between boolean algebras with operators and modal logic. (shrink)

In France, John Baptist Say has the merit of producing a very superior work on the subject of Political Economy. His arrangement is luminous, ideas clear, style perspicuous, and the whole subject brought within half the volume of [Adam] Smith's work. Add to this considerable advances in correctness and extension of principles.

As a futuristic emblem, smart cities represent a goal to provide all of the services required for a high-quality existence while conserving natural resources to the maximum extent possible. It turns out that the "Line City in Saudi Arabia" is the most famous and modern of these smart cities in terms of preserving 100 percent natural life, owing to the fact that they rely totally on natural energy and do not use any automobiles. The issues and challenges that have been (...) highlighted will assist in the improvement of municipal management. One of the most generally implemented projects in the field of smart cities is the technological and integrative developments of the use of sensors and data collecting in conjunction with rising difficulties aimed at enhancing human well-being and improving human livelihood. This is especially true in Saudi Arabia, where visitors can arrive quickly by just walking through the checkpoints, resulting in a journey of little more than a few minutes to reach any regular destination. It also splits the city into many different levels of the ground, enabling for the conservation of natural excess energy. (shrink)

FROM POLITICS TO THE MARKETPLACE, FEAR PLAYS AN INCREASINGLY important role in American culture. It shapes decisions as well as character, while it feeds an "ethic of security" that raises personal and national safety to the status of highest good. How might Christians respond faithfully to a culture of fear? This essay draws on Thomas Aquinas' account of fear in the Summa Theologica to provide a set of analytical categories and diagnostic questions in hopes of helping us become more reflective (...) about fear. At the very least, this discussion seeks to reintroduce the premodern categories of ordered and disordered fear to challenge the modern presumption that fear is a pre-political "given" in its twin forms of anxiety and terror. (shrink)

SC, CA, QA and QEA denote the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasi-polyadic algebras and quasi-polyadic equality algebras, respectively. Let ω ≤ α < β and let K ∈ {SC,CA,QA,QEA}. We show that the class of α -dimensional neat reducts of algebras in Kβ is not elementary. This solves a problem in [3]. Also our result generalizes results proved in [2] and [3].

We survey various results on the relationship among neat embeddings (a notion special to cylindric algebras), complete representations, omitting types, and amalgamation. A hitherto unpublished application of algebraic logic to omitting types of first-order logic is given.

We consider countable so‐called rich subsemigroups of ; each such semigroup T gives a variety CPEAT that is axiomatizable by a finite schema of equations taken in a countable subsignature of that of ω‐dimensional cylindric‐polyadic algebras with equality where substitutions are restricted to maps in T. It is shown that for any such T, if and only if is representable as a concrete set algebra of ω‐ary relations. The operations in the signature are set‐theoretically interpreted like in polyadic equality set (...) algebras, but such operations are relativized to a union of cartesian spaces that are not necessarily disjoint. This is a form of guarding semantics. We show that CPEAT is canonical and atom‐canonical. Imposing an extra condition on T, we prove that atomic algebras in CPEAT are completely representable and that CPEAT has the super amalgamation property. If T is rich and finitely represented, it is shown that CPEAT is term definitionally equivalent to a finitely axiomatizable Sahlqvist variety. Such semigroups exist. This can be regarded as a solution to the central finitizability problem in algebraic logic for first order logic with equality if we do not insist on full fledged commutativity of quantifiers. The finite dimensional case is approached from the view point of guarded and clique guarded (relativized) semantics of fragments of first order logic using finitely many variables. Both positive and negative results are presented. (shrink)

The Power of Sovereignty attempts to understand the ideas and thoughts of Sayyid Qutb whose corpus of work and, in particular, his theory of hakimiyyah (sovereignty) is viewed as a threat to nationalistic government and peace worldwide. This book provides a detailed perspective of Sayyid Qutb's writings."--Jacket.

Looking at the operation of forming neat $\alpha $ -reducts as a functor, with $\alpha $ an infinite ordinal, we investigate when such a functor obtained by truncating $\omega $ dimensions, has a right adjoint. We show that the neat reduct functor for representable cylindric algebras does not have a right adjoint, while that of polyadic algebras is an equivalence. We relate this categorial result to several amalgamation properties for classes of representable algebras. We show that the variety of cylindric (...) algebras of infinite dimension, endowed with the merry go round identities, fails to have the amalgamation property answering a question of Németi’s. We also study two variants of the so-called cylindric polyadic algebras introduced by Ferenczi (all are reducts of polyadic equality algebras, that are also varieties). We show that one is more cylindric than polyadic, and that the other is more polyadic than cylindric. Our classification is determined by results on neat embeddings and amalgamation expressed from the point of view of category theory, thereby witnessing, and, indeed, further emphasizing, the dichotomy between the cylindric and polyadic paradigms. For example, the first class does not have the unique neat embedding property, fails to have the amalgamation property and the neat reduct functor does not have a right adjoint, while the second class has the unique neat emdedding property, the superamalgamation property and the neat reduct functor is strongly invertible. Other results, like first order definability of the class of neat reducts and the class of completely representable algebras, confirming our classification along these lines are presented. (shrink)

We present a property of neat reducts commuting with forming subalgebras as a definability condition.

Let \(2 (...) It is shown that \(\mathbf{K_n}\) is not finitely axiomatizable and that it coincides with the class of atomic algebras in the elementary closure of \(\mathbf{S_c}{\sf Nr}_n{\sf CA}_{\omega}\) where \(\mathbf{S_c}\) is the operation of forming complete subalgebras. For any class \(\mathbf{L}\) such that \({\sf At}{\sf Nr}_n{\sf CA}_{\omega}\subseteq \mathbf{L}\subseteq {\sf At}\mathbf{K_n}\), it is proved that \({\bf SP}\mathfrak{Cm}\mathbf{L}={\sf RCA}_n\), where \({\sf Cm}\) is the dual operator to \(\sf At\); that of forming complex algebras. It is also shown that any class \(\mathbf{K}\) between \({\sf CRCA}_n\cap \mathbf{S_d}{\sf Nr}_n{\sf CA}_{\omega}\) and \(\mathbf{S_c}{\sf Nr}_n{\sf CA}_{n+3}\) is not first order definable, where \(\mathbf{S_d}\) is the operation of forming dense subalgebras, and that for any \(2shrink)

La 4ème de couv. indique : "Si l'on parcourt les oeuvres complètes Michael Sandel, il va sans dire que le leitmotiv de tout son argumentaire moral et politique est bien sa critique récurrente et massive de l'individu libéral et son corollaire sine qua non la neutralité politique. Ce que Michael Sandel s'efforce d'entreprendre dans sa critique de la "Théorie de la justice de Rawls", et à travers elle toute la tradition libérale qui prend son point d'appui dans le kantisme, est (...) précisément de dégager ce qui constitue sa force, à savoir les valeurs individualistes - fondements des démocraties libérales - qu'elle véhicule. Le (sic) gravité de l'individualisme libéral, tirant sa force de la rationalité subjective moderne, ne réside pas tant dans le caractère indiscutable des libertés fondamentales qu'il défend, mais dans la priorité morale et politique irréversible de l'individu qu'il instaure par opposition à la communauté historique. Cet individualisme méthodologique n'aurait pas pu s'installer pour Sandel avec autant de force sans le soutien de la neutralité politique, l'exclusion des conceptions du bien de l'espace public ; et ce, au profit de l'avènement de la "société marchande" qu'annonce le triomphalisme du marché.". (shrink)

The philosophy of Bruno Latour has given us one of the most important statements on the part played by technology in the ordering of the human collective. Typically presented as a radical departure from mainstream social thought, Latour is not without his intellectual creditors: Michel Serres and, through him, René Girard. By tracing this development, we are led to understand better the relationship of Latour’s work, and Actor-Network Theory more generally, to traditional sociological concerns. By doing so we can also (...) hope to understand better the role that objects play in structuring society. (shrink)

We construct an atomic uncountable theory with no prime models. This contrasts with the countable case.