The COVID-19 challenge is unprecedented. It has caused enormous trauma, disrupted economies, social life, mass transportation, work and employment, supply chains, leisure, sport, international relations, academic programmes; literally everything. Churches and religious communities have not been spared; they have been severely affected and, in all likelihood, permanently transformed by the pandemic. The pre-COVID-19 world is gone, replaced by a ‘new normal’. The new landscape calls for both resilience and adaptation, embracing new ways of doing things and of being church. Churches (...) have to adapt; they have to ask themselves questions about the implications for being church in this ‘new normal’ context. This article aims to explore the impact of the coronavirus on the mission and theology of the church. (shrink)

It is known Hrushovski and Pillay that a group G definable in the field \ of p-adic numbers is definably locally isomorphic to the group \\) of p-adic points of a algebraic group H over \. We observe here that if H is commutative then G is commutative-by-finite. This shows in particular that any one-dimensional group G definable in \ is commutative-by-finite. This result extends to groups definable in p-adically closed fields. We prove our results in the more general (...) context of geometric structures. (shrink)

The future of a black theology of liberation has been in question since the demise of apartheid in South Africa. The constitution of democracy in the country has raised questions about the relevance and purpose of such a theology in the wake of a new dispensation. Can we continue to promote the idea of ‘blackness’ in a democratic South Africa? Extracting from the contributions of the late Professor Vuyani Vellem, and as a tribute to his work, this article aims to (...) show that BTL definitely has a valid role for relevance and continuity. The author conducts a literature review of the material produced by Vuyani Vellem and identifies the emerging trends in which BTL continues to be alive and relevant.Contribution: The scholarly contribution of this article is its focus on the systematic and practical reflection, within a paradigm in which the intersection of religious studies, social sciences and humanities generate an interdisciplinary contested discourse. (shrink)

We study type-definable subgroups of small index in definable groups, and the structure on the quotient, in first order structures. We raise some conjectures in the case where the ambient structure is o-minimal. The gist is that in this o-minimal case, any definable group G should have a smallest type-definable subgroup of bounded index, and that the quotient, when equipped with the logic topology, should be a compact Lie group of the "right" dimension. I give positive answers to the conjectures (...) in the special cases when G is 1-dimensional, and when G is definably simple. (shrink)

In this paper we introduce the notion of a first order topological structure, and consider various possible conditions on the complexity of the definable sets in such a structure, drawing several consequences thereof.Our aim is to develop, for a restricted class of unstable theories, results analogous to those for stable theories. The “material basis” for such an endeavor is the analogy between the field of real numbers and the field of complex numbers, the former being a “nicely behaved” unstable structure (...) and the latter the archetypal stable structure. In this sense we try here to situate our work ono-minimal structures [PS] in a general topological context. Note, however, that thep-adic numbers, and structures definable therein, will also fit into our analysis.In the remainder of this section we discuss several ways of studying topological structures model-theoretically. Eventually we fix on the notion of a structure in which the topology is “explicitly definable” in the sense of Flum and Ziegler [FZ]. In §2 we introduce the hypothesis that every definable set is a Boolean combination of definable open sets. In §3 we introduce a “dimension rank” on definable sets. In §4 we consider structures on which this rank is defined, and for which also every definable set has a finite number of definably connected definable components. We show that prime models over sets exist under such conditions. (shrink)

We give a commentary on Newelski's suggestion or conjecture [8] that topological dynamics, in the sense of Ellis [3], applied to the action of a definable group $G(M)$ on its “external type space” $S_{G,\textit{ext}}(M)$, can explain, account for, or give rise to, the quotient $G/G^{00}$, at least for suitable groups in NIP theories. We give a positive answer for measure-stable (or $fsg$) groups in NIP theories. As part of our analysis we show the existence of “externally definable” generics of $G(M)$ (...) for measure-stable groups. We also point out that for $G$ definably amenable (in a NIP theory) $G/G^{00}$ can be recovered, via the Ellis theory, from a natural Ellis semigroup structure on the space of global $f$-generic types. (shrink)

For a countable complete o-minimal theory T, we introduce the notion of a sequentially complete model of T. We show that a model M of T is sequentially complete if and only if $\mathscr{M} \prec \mathscr{N}$ for some Dedekind complete model N. We also prove that if T has a Dedekind complete model of power greater than 2 ℵ 0 , then T has Dedekind complete models of arbitrarily large powers. Lastly, we show that a dyadic theory--namely, a theory relative (...) to which every formula is equivalent to a Boolean combination of formulas in two variables--that has some Dedekind complete model has Dedekind complete models in arbitrarily large powers. (shrink)

We continue the study of simple theories begun in [3] and [5]. We first find the right analogue of definability of types. We then develop the theory of generic types and stabilizers for groups definable in simple theories. The general ideology is that the role of formulas (or definability) in stable theories is replaced by partial types (or ∞-definability) in simple theories.

The notion of CM-triviality was introduced by Hrushovski, who showed that his new strongly minimal sets have this property. Recently Baudisch has shown that his new ω 1 -categorical group has this property. Here we show that any group of finite Morley rank definable in a CM-trivial theory is nilpotent-by-finite, or equivalently no simple group of finite Morley rank can be definable in a CM-trivial theory.

We introduce and study the notions of a PAC-substructure of a stable structure, and a bounded substructure of an arbitrary substructure, generalizing [10]. We give precise definitions and equivalences, saying what it means for properties such as PAC to be first order, study some examples (such as differentially closed fields) in detail, relate the material to generic automorphisms, and generalize a "descent theorem" for pseudo-algebraically closed fields to the stable context. We also point out that the elementary invariants of pseudo-algebraically (...) closed fields from [6] are also valid for pseudo-differentially closed fields. (shrink)

Les corps algébriquement clos, réels clos et pseudo-finis n'ont, pour chaque entier n, qu'un nombre fini d'extensions de degré n; nous montrons qu'ils partagent cette propriété avec tous les corps qui, comme eux, satisfont une propriété très rudimentaire de préservation de la dimension, de nature modèle-théorique. Ce résultat est atteint en montrant qu'une certaine action du groupe GLn d'un tel corps n'a qu'un nombre fini d'orbites. /// La korpoj algebre fermataj, reale fermataj kaj pseudofinataj ne havas, pri ciu integro n, (...) pli ol finitan nombron de sternejoj kun grado n; ni montras ke ili kunpartigas tiu ci propecon kun ciu tiel korpoj kiuj kontentigas kiel ili unu tre simplan modelteorian propecon de konserveco de la amplekso. Pri atingi la resultaton, ni montras ke kelka ago de la grupo GLn de tiel korpo havas sole finitan nombron de orbitoj. (shrink)

Given a lovely pair P ≺ M of models of a simple theory T, we study the structure whose universe is P and whose relations are the traces on P of definable (in ℒ with parameters from M) sets in M. We give a necessary and sufficient condition on T (which we call weak lowness) for this structure to have quantifier-elimination. We give an example of a non-weakly-low simple theory.

Care of the critically ill newborn includes support for the birth mother/parents with regular updates around the clinical condition of the baby, and involvement in discussions around complex decision-making issues. Discussions around continuation or discontinuation of life-sustaining are challenging even in the most straightforward of cases, but what happens when the birth mother is critically unwell? Such cases can lead to uncertainty around who should assume the parental role for these difficult discussions. In this round table discussion, we explore the (...) ethical, moral and legal uncertainties raised by coincident severe maternal and neonatal illness in the context of surrogacy. (shrink)

We consider the theory P of pairs F (...) is generically free. (shrink)

Adequate measurement is an essential component of the assessment of mental health disorders and symptoms such as depression and anxiety. The present study investigated sex-specific differences in the Patient Health Questionnaire-9 and Generalized Anxiety Disorder-7. This comprehensive cross-sectional design study pursued four objectives: measurement invariance of PHQ-9 and GAD-7 between male and female; depression and anxiety prevalence differences; cross-sex differences in the relationship between depression and anxiety; and a comparison of symptom heterogeneity. A sample of 1966 students from South Africa (...) completed the PHQ-9 and the GAD-7. Data analyses for measurement invariance, latent class analysis, inter-variable correlations and group comparisons were conducted in Mplus. The two-dimensional PHQ-9 achieved scalar invariance, while the GAD-7 yielded metric invariance. The somatic and non-somatic latent dimensions of depression were compared and showed no significant difference between male and female groups. The positive relationship between depression and anxiety was also not significantly different between the two groups. While the PHQ-9 symptoms formed three classes in the male group, and four classes in the female group, the GAD-7 had the same number of classes and a similar pattern between the two groups. These findings hold implications for the measurement, assessment and understanding of symptom manifestation and distribution, as well as the treatment of depression and anxiety in South Africa. (shrink)

Morley rank and Lascar rank are equal on generic types of definable groups in differentially closed fields with finitely many commuting derivations.

Many Christians feel quite disillusioned and disappointed with the church in South Africa today because they assume that the church, in particular the South African Council of Churches, is not playing an adequate prophetic role in building the democratic South Africa since 1994. This article traces the role and contributions of the SACC and other ecumenical organisations to the building of a democratic South Africa. It establishes that whilst the SACC had lost its focus and vision and has an ecumenical (...) body, largely because of its partnership with government, it does, nevertheless, continue to contribute to the building of the South African nation. (shrink)

South African universities are in the process of serious transformation and restructuring. The place of faculties of theology at universities has come under the spotlight resulting in the closure of several theological faculties or in the moving of theology to other faculties, mainly humanities or arts. Theology is under pressure and in the current academic environment, Church History, in its traditional form, has all but disappeared from South African universities. This article is an attempt to address the current situation. Whilst (...) this article looks at the issue of theology at public universities, its main focus is to explore the future study of church history in the context of universities and, in particular, a Faculty of Theology. Understanding church history in the broad framework as Historical Theology, this article asserts the significance of church history at public universities, but points out the need to restructure the Department giving due consideration to community engagement, internationalisation, transformation, africanisation and interreligious collaboration. All of these would have a serious impact on teaching, learning and research. (shrink)

We develop “local NIP group theory” in the context of pseudofinite groups. In particular, given a sufficiently saturated pseudofinite structure G expanding a group, and left invariant NIP formula δ...

For G a group definable in some structure M, we define notions of “definable” compactification of G and “definable” action of G on a compact space X , where the latter is under a definability of types assumption on M. We describe the universal definable compactification of G as View the MathML source and the universal definable G-ambit as the type space SG. We also point out the existence and uniqueness of “universal minimal definable G-flows”, and discuss issues of amenability (...) and extreme amenability in this definable category, with a characterization of the latter. For the sake of completeness we also describe the universal compactification and universal G-ambit in model-theoretic terms, when G is a topological group. (shrink)

We prove that any countable simple unidimensional theory T is supersimple, under the additional assumptions that T eliminates hyperimaginaries and that the $D_\phi-ranks$ are finite and definable.

We discuss the close relationship between structural theorems in (generalized) stability theory, and graph regularity theorems.

We extend Morley's Theorem to show that if a theory is κ-p-categorical for some uncountable cardinal κ, it is uncountably categorical. We then discuss ω-p-categoricity and provide examples to show that similar extensions for the Baldwin-Lachlan and Lachlan Theorems are not possible.

We clarify and correct some statements and results in the literature concerning unimodularity in the sense of Hrushovski [7], and measurability in the sense of Macpherson and Steinhorn [8], pointing out in particular that the two notions coincide for strongly minimal structures and that another property from [7] is strictly weaker, as well as "completing" Elwes' proof [5] that measurability implies 1-basedness for stable theories.

We characterize the non-modular models of a unidimensional first-order theory of modules as the elementary submodels of its prime pure-injective model. We show that in case the maximal non-modular submodel of a given model splits off this is true for every such submodel, and we thus obtain a cancellation result for this situation. Although the theories in question always have models whose maximal non-modular submodel do split off, they may as well have others where they don't. We present a corresponding (...) example. (shrink)

We initiate an account of Shelah’s notion of “strong dependence” in terms of generically stable measures, proving a measure analogue of the fact that a stable theory $T$ is “strongly dependent” if and only if all types have almost finite weight.

A lay movement known as the Poor of Christ, incorrectly referred to as the Waldensians, started in the Roman Church in 1176 and rapidly spread through Europe despite severe persecution by the church. Through their values and methods, they impacted on the communities where they were present. This article aims to show their role and contributions indicating its impact on the 16th century Reformation and relevance for the church today. It does this by examining selected themes from the Poor of (...) Christ: their life-transforming faith, the strengthening of laity, the equal role of women in ministry, the importance of teaching and living the faith, a focused rather than fenced theology and loyalty to the one Church of Christ. The article also draws reference to the COVID-19 pandemic and explores what we can learn from the Poor of Christ in addressing this situation.Contribution: This article puts the spotlight on an overlooked lay movement that contributed significantly in preparing the climate for the 16th Century Reformation. Their example shows that the real strength of church is through members empowered to holistically live their faith. The article shows the current relevance of their values and methods. (shrink)

This article engaged in critical analyses of the capitalistic nature of the practices of African Neo-Pentecostal leaders with a focus on a few but most popular Nigerian and South African Neo-Pentecostal leaders. Using Julius Nyerere's African moral philosophy called Ujamaa, the article viewed and critiqued the narratives with an emphasis on how antithetical such practices are to the communitarian nature of African society which provides for people-centred servant leadership. Progressively, the article discovered that such capitalistic practices promote manipulative, exploitative and (...) inhuman culture and therefore engenders gross socio-moral and socio-economic abuse of the rights and privileges of millions of Church adherents. It further deduced that amongst others, lack of love towards the adherents and surrounding communities is at the heart of such bankrupt practices and therefore recommended the three principles and three factors of Ujamaa's philosophy as essential values needed for the transformation of the Neo-Pentecostal religious organisations or nations. It is the conclusive remark of this article that every leader needs to adopt Ujamaa's philosophy as a basic leadership requirement for communitarian and people-centred service to humanity. CONTRIBUTION: Aligning with HTS Teologiese Studies/Theological Studies focus and scope, this article contributed to an interdisciplinary religious aspect of research as it brought forward the interplay of African Moral Philosophy and African Pentecostal Theology aimed at discovering pathways to improve the African Christian leaders' socio-moral and socio-economic services to adherents and African communities at large. (shrink)

First, it is pointed out how the author's new differential Galois theory contributes to the understanding of the differential closure of an arbitrary differential field . Secondly, it is shown that a superstable differential field has no proper differential Galois extensions.

Edward Said's book Orientalism stands in a long lineage of critique of European scholarship responsible for shaping European understandings of foreign cultures. His book contributed significantly to the debate about the epistemological presuppositions informing European scholars of other cultures. However, while Said exposed in considerable detail the ways in which the Orient was distorted by the theories of the European academy, he left unexamined the possibility of genuine cross-cultural understanding. This article considers the significance of hermeneutics for cross-cultural rather than (...) historical understanding. It explores the implicit claim Gadamer makes for the universal validity of hermeneutics not only for understanding in history, but for a genuine intellectual rapprochement across geographical and cultural lines as well. S. Afr. J. Philos. Vol.21(4) 2002: 330-344. (shrink)