Books reviewed:Renate Egger‐Wenzel, Ben Sira's GodPaul J. Achtemeier, Joel B. Green and Marianne Meye Thompson, Introducing the New Testament, Its Literature and TheologyI. Boxall, Revelation: Vision and Insight. An Introduction to the ApocalypseS. Moyise, Studies in the Book of RevelationG. R. Osborne, Revelation: The Baker Exegetical Commentary on the New TestamentN. T. Wright, The Resurrection of the Son of GodGillian Clark and T. Rajak, Philosophy and Power in the Graeco‐Roman World: Essays in Honour of Miriam GriffinRichard Paul Vaggione, Eunomius of (...) Cyzicus and the Nicene RevolutionStephen T. Davies, Daniel Kendall S. J. and Gerald O'Collins, The Incarnation. An Interdisciplinary Symposium on the Incarnation of the Son of GodRichard Cross, The Metaphysics of the IncarnationHugh Connolly, SinAnthony W. Bartlett, Cross Purposes: The Violent Grammar of Christian AtonementStanley Hauerwas, With the Grain of the Universe: The Church's Witness and Natural TheologySarah Coakley, Powers and Submissions: Spirituality, Philosophy and GenderChristopher Cocksworth and Rosalind Brown, Being a Priest Today: Exploring priestly identityRandall Balmer, Encyclopedia of EvangelicalismKate Armstrong, Crisis and RepetitionAnthony A. Barrett, Livia: First Lady of Imperial RomeGerhard Podskalsky, Von Photios zu Bessarion: Der Vorrang humanistisch geprägter Theologie in Byzanz und deren bleibende BedeutungNicola Coldstream, Medieval ArchitectureW. J. Armstrong, J. A. W. Hellmann and W. Short, Francis of Assisi: Early Documents, IIIEllen E. Kittell and Thomas F. Madden, Medieval and Renaissance VeniceTheodor Dieter, Der junge Luther und Aristoteles: Eine historisch‐systematische Untersuchung zum Verhältnis von Theologie und PhilosophieAndrew Brown, Church and Society in England, 1000–1500Renate Blumenfeld‐Kosinski, Duncan Robertson, and Nancy Warren, The Vernacular Spirit: Essays on Medieval Religious LiteratureBarry Collett, Female Monastic Life in Early Tudor England, with an Edition of Richard Fox's Translation of the Benedictine Rule for Women, 1517Marc R. Forster, The Catholic Revival in the Age of the Baroque. Religious Identity in Southwest Germany, 1550–1750W. R. Ward, Christianity under the Ancien Régime 1648–1789Nigel Aston, Religion and Revolution in France 1780–1804Catharine Edwards, Roman Presences: Receptions of Rome in European Culture, 1789–1945Bruce L. Kinzer, England's Disgrace? J. S. Mill and the Irish QuestionJohn Corrigan, Business of the Heart: Religion and Emotion in the Nineteenth CenturyPeter M. Chisnall, John Henry Cardinal Newman: A Man of Courage, Conflict and ConvictionVincent Ferrer Blehl, Pilgrim Journey: John Henry Newman 1801–1845Kester Aspden, Fortress Church. The English Roman Catholic Bishops and Politics 1903–63David Alvarez, Spies In The Vatican: Espionage and Intrigue From Napoleon to the HolocaustPeter McDonough and Eugene C. Bianchi, Passionate Uncertainty: Inside the American JesuitsRuby Blondell, The Play of Character in Plato's Dialogues. (shrink)

A recursively enumerable splitting of an r.e. setAis a pair of r.e. setsBandCsuch thatA=B∪CandB∩C= ⊘. Since for such a splitting degA= degB∪ degC, r.e. splittings proved to be a quite useful notion for investigations into the structure of the r.e. degrees. Important splitting theorems, like Sacks splitting [S1], Robinson splitting [R1] and Lachlan splitting [L3], use r.e. splittings.Since each r.e. splitting of a set induces a splitting of its degree, it is natural to study the relation between the degrees of (...) r.e. splittings and the degree splittings of a set. We say a setAhas thestrong universal splitting property if each splitting of its degree is represented by an r.e. splitting of itself, i.e., if for degA=b∪cthere is an r.e. splittingB, CofAsuch that degB=band degC=c. The goal of this paper is the study of this splitting property.In the literature some weaker splitting properties have been studied as well as splitting properties which imply failure of the SUSP. (shrink)

Name der Zeitschrift: Zeitschrift für Religionswissenschaft Jahrgang: 25 Heft: 2 Seiten: 263-286.

Ambos-Spies, K. and R.A. Shore, Undecidability and 1-types in the recursively enumerable degrees, Annals of Pure and Applied Logic 63 3–37. We show that the theory of the partial ordering of recursively enumerable Turing degrees is undecidable and has uncountably many 1-types. In contrast to the original proof of the former which used a very complicated O''' argument our proof proceeds by a much simpler infinite injury argument. Moreover, it combines with the permitting technique to get similar results for (...) any ideal of the r.e. degrees. (shrink)

We prove that every Turing degree a bounding some non-GL₂ degree is recursively enumerable in and above (r.e.a.) some 1-generic degree.

In Reverse Mathematics, the axiom system DNR, asserting the existence of diagonally non-recursive functions, is strictly weaker than WWKL0.

We solve a longstanding question of Soare by showing that if ${\mathbf d}$ is a non-low $_2$ computably enumerable degree then ${\mathbf d}$ contains a c.e. set with no r-maximal c.e. superset.

We give a decision procedure for the ∀∃-theory of the weak truth-table (wtt) degrees of the recursively enumerable sets. The key to this decision procedure is a characterization of the finite lattices which can be embedded into the r.e. wtt-degrees by a map which preserves the least and greatest elements: a finite lattice has such an embedding if and only if it is distributive and the ideal generated by its cappable elements and the filter generated by its cuppable elements are (...) disjoint. We formulate general criteria that allow one to conclude that a distributive upper semi-lattice has a decidable two-quantifier theory. These criteria are applied not only to the weak truth-table degrees of the recursively enumerable sets but also to various substructures of the polynomial many-one (pm) degrees of the recursive sets. These applications to the pm degrees require no new complexity-theoretic results. The fact that the pm-degrees of the recursive sets have a decidable two-quantifier theory answers a question raised by Shore and Slaman in [21]. (shrink)

Hence, there is still controversy over which of the two versions of the deduction deserves priority and whether indeed any distinction between them can be maintained that would go beyond questions of presentation and involve the structure of the proof itself. Schopenhauer and Heidegger held that the first edition alone fully expresses Kant's unique philosophy, while Kant himself, as well as many other Kantians, have only seen a difference in the method of presentation.

The changes that have taken place in Ukrainian Protestantism since the independence of the country have repeatedly attracted the attention of domestic religious scholars. V. Yelensky, V. Lyubashchenko, O. Nazarkina, Y. Reshetnikov, V. Titarenko, V. Franchuk, P. Yarotsky, TV, addressed the problem in their works. Further analysis, however, is greatly complicated by the lack of empirical material that would be accompanied by primary interpretations.

Review text: "... ist diese Einführung als solche uneingeschränkt zu empfehlen, da sie ihrem "analytischen? Charakter im besten Sinne des Wortes gerecht wird."Werner Wolbert in: Salzburger Theologische Zeitschrift 2/2008.

We show that, in the partial ordering of the computably enumerable computable Lipschitz degrees, there is a degree a>0a>0 such that the class of the degrees which do not cup to a is not bounded by any degree less than a. Since Ambos-Spies [1] has shown that, in the partial ordering of the c.e. identity-bounded Turing degrees, for any degree a>0a>0 the degrees which do not cup to a are bounded by the 1-shift a+1a+1 of a where a+1 (...) follows that the elementary theories of the partial orderings and differ. (shrink)

We show that the partial order of Σ0 3-sets under inclusion is elementarily definable with parameters in the semilattice of r.e. wtt-degrees. Using a result of E. Herrmann, we can deduce that this semilattice has an undecidable theory, thereby solving an open problem of P. Odifreddi.

Name der Zeitschrift: Semiotica Jahrgang: 2014 Heft: 202 Seiten: 321-343.

Downey and Lempp 1215–1240) have shown that the contiguous computably enumerable degrees, i.e. the c.e. Turing degrees containing only one c.e. weak truth-table degree, can be characterized by a local distributivity property. Here we extend their result by showing that a c.e. degree a is noncontiguous if and only if there is an embedding of the nonmodular 5-element lattice N5 into the c.e. degrees which maps the top to the degree a. In particular, this shows that local nondistributivity coincides with (...) local nonmodularity in the computably enumerable degrees. (shrink)

It is shown that, if a, b are recursively enumerable degrees such that 0

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We give a simple structural property which characterizes the r.e. sets whose (Turing) degrees are cappable. Since cappable degrees are incomplete, this may be viewed as a solution of Post's program, which asks for a simple structural property of nonrecursive r.e. sets which ensures incompleteness.

We explore the complexity of Sacks’ Splitting Theorem in terms of the mind change functions associated with the members of the splits. We prove that, for any c.e. set A, there are low computably enumerable sets $A_0\sqcup A_1=A$ splitting A with $A_0$ and $A_1$ both totally $\omega ^2$ -c.a. in terms of the Downey–Greenberg hierarchy, and this result cannot be improved to totally $\omega $ -c.a. as shown in [9]. We also show that if cone avoidance is added then there (...) is no level below $\varepsilon _0$ which can be used to characterize the complexity of $A_1$ and $A_2$. (shrink)

Globalization processes mean, among other things, the spread of trends that determine the socio-religious development of a region to other spatial areas. This does not happen with an inevitable necessity, it is not a ubiquitous feature of globalization, but it does happen with a very high probability. Moreover, when it comes to development within the same confessional systems. In this context, it is pertinent to note that some of the widespread forms of religious practices in Ukraine today, and moreover, religious (...) structures, fifteen or twenty years ago, seemed to be exclusively Western. This is especially true of the large number of denominations, movements and movements that are Protestant in origin and are referred to as "evangelical" in English literature. (shrink)

We show that the theory of the partial ordering of the computably enumerable degrees in any given nontrivial interval is undecidable and has uncountably many 1-types.

My presentation begins with Kant's philosophical project, which played a key role in understanding German Idealism, and then considers in detail the philosophical approaches developed by Schelling and Hegel.