A coordinate-free formulation is established for (semi) classical particle-field interactions. The exterior language of spacetime chains and De-Rham currents enables the description to include extended strings and membranes besides point particles. Treating physical fields in terms of sections of particular bundles, a unified account of interactions is presented in terms of an intrinsic action principle on a bundle of jets over spacetime. The theory is illustrated by considering the specific model of point particles with intrinsic spin covariantly coupled to theU(1) (...) andSL(2, C) connections describing the electromagnetic and gravitational fields, respectively. The notion of dual spin is examined in this context and coupled equations for this particle-field system are explicitly derived in a local chart. Attention is drawn to the global implications of the theory. (shrink)

We are told that when news of Caracalla's death reached Rome a group of senators denounced their former emperor, likening him to all the tyrants of the past who had ruled over them. The senator who recorded these actions, the historian Cassius Dio, does not say which tyrants were listed, but it is likely that such a comprehensive list included the last king of Rome, Tarquinius Superbus, and his son Sextus. The senators' actions were doubtless more an act of group (...) catharsis than a private show of loyalty to their new emperor, Marcus Opellius Macrinus. Yet what the scene reveals perhaps most clearly is the Romanexemplatradition in practice. (shrink)

The kleptocratic supremacy of the praetorian prefect C. Fulvius Plautianus was felt throughout the city of Rome, the Empire and even beyond the imperial frontiers. Indeed, for the senatorial historian Dio Cassius, there was no more picturesque demonstration of Plautianus' acquisitiveness than his seizure of strange striped horse-like creatures from ‘islands in the Erythraean Sea’. The passage, as preserved in the text of Xiphilinus' Epitome, reads as follows : καὶ τέλος ἵππους Ἡλίῳ τιγροειδεῖς ἐκ τῶν ἐν τῇ Ἐρυθρᾷ θαλάσσῃ νήσων, (...) πέμψας ἑκατοντάρχους, ἐξέκλεψεν·In the end he even stole tiger-like horses to Helios from the islands in the Erythraean Sea, having sent some centurions to carry out the task. (shrink)

A scholium in codex Vaticanus graecus 156 provides evidence that Cassius Dio's Roman History once contained an explicit reference to the ludi saeculares of a.d. 204, something that has been denied in recent scholarship.

We give a survey of the study of nonstandard models in recursion theory and reverse mathematics. We discuss the key notions and techniques in effective computability in nonstandard models. and their applications to problems concerning combinatorial principles in subsystems of second order arithmetic. Particular attention is given to principles related to Ramsey's Theorem for Pairs.