Dr. Cyril Bailey and Dr. C. M. Bowra have most recently analysed Virgil's method of using the expressions of Lucretius and Ennius respectively, and Mile A.-M. Guillemin has lately added significant considerations to Father F.-X. M. J. Roiron's long examination of Virgil's method of using again his own former expressions. Since then other work has been done with the purpose of clarifying the less rational part of Virgil's self-repetition; it might be called complementary to the well-known researches of Mr. John (...) Sparrow. With such a purpose I have tried to suggest how Virgil reached the strange phrase in the first Eclogue, rapidum Cretae, or cretae, Oaxen, by a not unparalleled confusion of the names of several different rivers and at least one town. (shrink)

For about a hundred years there has been an intermittent but sometimes vigorous debate1 on the question whether Quintus Smyrnaeus and Tryphiodorus directly used the Second Aeneid as a source for their epic descriptions “of the capture and destruction of Troy. Heyne thought that they did not; but towards the end of the nineteenth century it appeared more likely that they did. Heinze opposed the general belief: but it was reaffirmed for Quintus by Paschal and Becker4 and for Tryphiodorus by (...) Dr. E. Cesareo on internal evidence. Meanwhile Professor Samuel E. Bassett had concluded that Quintus was not after all dependent on Vergil: and still more recently Dr. J. W. Mackail, reviewing Cesareo's monograph, has maintained with emphasis that the Aeneid is certainly not the source of the late epic. Accordingly the controversy cannot even now be considered closed. (shrink)

For about a hundred years there has been an intermittent but sometimes vigorous debate1 on the question whether Quintus Smyrnaeus and Tryphiodorus directly used the Second Aeneid as a source for their epic descriptions “of the capture and destruction of Troy. Heyne thought that they did not; but towards the end of the nineteenth century it appeared more likely that they did. Heinze opposed the general belief: but it was reaffirmed for Quintus by Paschal and Becker4 and for Tryphiodorus by (...) Dr. E. Cesareo on internal evidence. Meanwhile Professor Samuel E. Bassett had concluded that Quintus was not after all dependent on Vergil: and still more recently Dr. J. W. Mackail, reviewing Cesareo's monograph, has maintained with emphasis that the Aeneid is certainly not the source of the late epic. Accordingly the controversy cannot even now be considered closed. (shrink)

It is sufficiently probable that quantitative scansion in Latin, imposed on a language in which accentuation by stress was alone significant originally, not only gave way to the earlier principle in the decline of Latin literature, but scarcely tended to suppress it at any time in common speech and in familiar writing. It is also probable therefore that even in literature dominated by quantity stress-accentuation was not obliterated altogether. In fact the incidences of it, in Vergilian verse at least, seemed (...) so characteristic that in late Antiquity the Vergilian stress-rhythms were apparently copied without any knowledge of the prosody of the hexameter. In modern expositions, the variety of Vergil's rhythms is generally referred, not only to scansion, but also to stress-accentuation: and it has recently been shown that lines in which stress and metrical ictus predominantly coincide are different in quality and expressiveness from lines in which they do not. Since however no general explanation or definition of this difference in quality seemed to have been offered, I lately attempted a simple theory which would account for the different aesthetic values of lines of these two classes, and which would define, if possible, what these different values are. (shrink)

It is sufficiently probable that quantitative scansion in Latin, imposed on a language in which accentuation by stress was alone significant originally, not only gave way to the earlier principle in the decline of Latin literature, but scarcely tended to suppress it at any time in common speech and in familiar writing. It is also probable therefore that even in literature dominated by quantity stress-accentuation was not obliterated altogether. In fact the incidences of it, in Vergilian verse at least, seemed (...) so characteristic that in late Antiquity the Vergilian stress-rhythms were apparently copied without any knowledge of the prosody of the hexameter. In modern expositions, the variety of Vergil's rhythms is generally referred, not only to scansion, but also to stress-accentuation: and it has recently been shown that lines in which stress and metrical ictus predominantly coincide are different in quality and expressiveness from lines in which they do not. Since however no general explanation or definition of this difference in quality seemed to have been offered, I lately attempted a simple theory which would account for the different aesthetic values of lines of these two classes, and which would define, if possible, what these different values are. (shrink)

Computable structures of Scott rank ${\omega_1^{CK}}$ are an important boundary case for structural complexity. While every countable structure is determined, up to isomorphism, by a sentence of ${\mathcal{L}_{\omega_1 \omega}}$ , this sentence may not be computable. We give examples, in several familiar classes of structures, of computable structures with Scott rank ${\omega_1^{CK}}$ whose computable infinitary theories are each ${\aleph_0}$ -categorical. General conditions are given, covering many known methods for constructing computable structures with Scott rank ${\omega_1^{CK}}$ , which guarantee that the (...) resulting structure is a model of an ${\aleph_0}$ -categorical computable infinitary theory. (shrink)

This paper calculates, in a precise way, the complexity of the index sets for three classes of computable structures: the class $K_{\omega _{1}^{\mathit{CK}}}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}$ , the class $K_{\omega _{1}^{\mathit{CK}}+1}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}+1$ , and the class K of all structures of non-computable Scott rank. We show that I(K) is m-complete $\Sigma _{1}^{1},\,I(K_{\omega _{1}^{\mathit{CK}}})$ is m-complete $\Pi _{2}^{0}$ relative to Kleen's O, and $I(K_{\omega _{1}^{\mathit{CK}}+1})$ is m-complete $\Sigma _{2}^{0}$ relative to O.

Here we prove that if T and T′ are strongly minimal theories, where T′ satisfies a certain property related to triviality and T does not, and T′ is model complete, then there is no computable embedding of Mod(T) into Mod(T′). Using this, we answer a question from [4], showing that there is no computable embedding of VS into ZS, where VS is the class of infinite vector spaces over Q, and ZS is the class of models of Th(Z, S). Similarly, (...) we show that there is no computable embedding of ACF into ZS, where ACF is the class of algebraically closed fields of characteristic 0. (shrink)

We extend results of Harizanov and Barker. For a relation R on a recursive structure /oA, we give conditions guaranteeing that the image of R in a recursive copy of /oA can be made to have arbitrary ∑α0 degree over Δα0. We give stronger conditions under which the image of R can be made ∑α0 degree as well. The degrees over Δα0 can be replaced by certain more general classes. We also generalize the Friedberg-Muchnik Theorem, giving conditions on a pair (...) of relations R and S under which the images of R and S can be made ∑α0 and independent over Δα0 in a recursive copy of /oA. (shrink)

In this paper, we give an example of a complete computable infinitary theory T with countable models ${\mathcal{M}}$ and ${\mathcal{N}}$ , where ${\mathcal{N}}$ is a proper computable infinitary extension of ${\mathcal{M}}$ and T has no uncountable model. In fact, ${\mathcal{M}}$ and ${\mathcal{N}}$ are (up to isomorphism) the only models of T. Moreover, for all computable ordinals α, the computable ${\Sigma_\alpha}$ part of T is hyperarithmetical. It follows from a theorem of Gregory (JSL 38:460–470, 1972; Not Am Math Soc 17:967–968, 1970) (...) that if T is a Π 1 1 set of computable infinitary sentences and T has a pair of models ${\mathcal{M}}$ and ${\mathcal{N}}$ , where ${\mathcal{N}}$ is a proper computable infinitary extension of ${\mathcal{M}}$ , then T would have an uncountable model. (shrink)

Name der Zeitschrift: Neue Zeitschrift für Systematische Theologie und Religionsphilosophie Jahrgang: 57 Heft: 1 Seiten: 138-154.

Let be a recursive structure, and let R be a recursive relation on . Harizanov isolated a syntactical condition which is necessary and sufficient for to have recursive copies in which the image of R is r.e. of arbitrary r.e. degree. We had conjectured that a certain extension of Harizanov's syntactical condition would be necessary and sufficient for to have recursive copies in which the image of R is ∑α0 of arbitrary ∑α0 degree, but this is not the case. Here (...) we give examples illustrating some restrictions on the possible ∑α0 degrees. In these examples, the image of R cannot be ∑α0 of degree d unless d possesses an “α-table”. (shrink)

Ash and Nerode [2] gave natural definability conditions under which a relation is intrinsically r. e. Here we generalize this to arbitrary levels in Ershov's hierarchy of Δmath image sets, giving conditions under which a relation is intrinsically α-r. e.