bluuebunny/crossref_metadata_2025_split huggingface dataset:
New Dichotomies for Borel Equivalence Relations
Authors: Hjorth Greg , Kechris Alexander S. 
Published: May 2006

We announce two new dichotomy theorems for Borel equivalence relations, and present the results in context by giving an overview of related recent developments.§1. Introduction. For X a Polish (i.e., separable, completely metrizable) space and E a Borel equivalence relation on X, a (complete) classification of X up to E-equivalence consists of finding a set of invariants I and a map c : X → I such that xEy ⇔ c(x) = c(y). To be of any value we would expect I and c to be “explicit” or “definable”. The theory of Borel equivalence relations investigates the nature of possible invariants and provides a hierarchy of notions of classification.The following partial (pre-)ordering is fundamental in organizing this study. Given equivalence relations E and F on X and Y, resp., we say that E can be Borel reduced to F, in symbolsif there is a Borel map f : X → Y with xEy ⇔ f(x)Ff(y). Then if is an embedding of X/E into Y/F, which is “Borel” (in the sense that it has a Borel lifting).Intuitively, E ≤BF might be interpreted in any one of the following ways:(i) The classi.cation problem for E is simpler than (or can be reduced to) that of F: any invariants for F work as well for E (after composing by an f as above).(ii) One can classify E by using as invariants F-equivalence classes.(iii) The quotient space X/E has “Borel cardinality” less than or equal to that of Y/F, in the sense that there is a “Borel” embedding of X/E into Y/F.
Models of Second-Order Zermelo Set Theory
Authors: Uzquiano Gabriel 
Published: May 2006

In [12], Ernst Zermelo described a succession of models for the axioms of set theory as initial segments of a cumulative hierarchy of levelsUαVα. The recursive definition of theVα's is:Thus, a little reflection on the axioms of Zermelo-Fraenkel set theory (ZF) shows thatVω, the first transfinite level of the hierarchy, is a model of all the axioms ofZFwith the exception of the axiom of infinity. And, in general, one finds that ifκis a strongly inaccessible ordinal, thenVκis a model of all of the axioms ofZF. (For all these models, we take∈to be the standard element-set relation restricted to the members of the domain.) Doubtless, when cast as a first-order theory,ZFdoes not characterize the structures 〈Vκ,∈∩(Vκ×Vκ)〉 forκa strongly inaccessible ordinal, by the Löwenheim-Skolem theorem. Still, one of the main achievements of [12] consisted in establishing that a characterization of these models can be attained when one ventures into second-order logic. For let second-orderZFbe, as usual, the theory that results fromZFwhen the axiom schema of replacement is replaced by its second-order universal closure. Then, it is a remarkable result due to Zermelo that second-orderZFcan only be satisfied in models of the form 〈Vκ,∈∩(Vκ×Vκ)〉 forκa strongly inaccessible ordinal.
Two Archaic Greek Sarcophagi
Authors: Dennis George 
Published: May 2006

These sarcophagi were brought to light by accident in the summer of 1882, by peasants digging in the fields. Hearing of the discovery I made an attempt to purchase them, but before my negotiations were completed, the Ottoman authorities stepped in and appropriated the monuments, which are now lying in a porch of the Governor General's palace, much injured by the rough handling they have received in their transport to Smyrna.These sarcophagi possess a peculiar interest as presenting to us the only specimens of local pictorial art of an early Greek period as yet discovered on the coast of Asia Minor. It is a singular fact that no figured vases, so far as I can learn, have been disinterred on this coast, save a few of small size and insignificant character found in the Troad, and two amphorae of a late period discovered by Mr. Newton in the necropolis of Halicarnassus (Discoveries in the Levant, vol. ii. p. 63). The scarcity of such vases seems to suggest that these exceptions had probably been imported, as we know that Greek vases were articles of commerce in ancient times (Plin. H. N. xxxv. 46); but these sarcophagi from their size, weight, and material cannot have been other than of local manufacture and adornment, and are the only monuments which afford us a knowledge of Ionian pictorial art at a period before Herodotus wrote or Pindar sung, and, it may be, before Anacreon fled from the neighbouring city of Teos to sing the praises of love and wine at the court of Polycrates.
On the Syrinx (σȗριγξ) in the Ancient Chariot
Authors: Verrall A. W. 
Published: May 2006

The Attic Tragedians—for the use seems to have extant examples there only—several times apply the word σȗριγξ to the wheel of a chariot or some part of it. The passages are these:—Aesch. Supp. 181:Id. Sept. 205:Soph. Electra, 720:Eur. Hipp. 1234:Id. Iph. A. 227:The current explanation of the word in this application is given by Liddell and Scott thus: ‘σȗριγξ, II., anything like a pipe; 1. a spear-case = δορατοθήκη, II. 19, 387. 2. the box or hole in the nave of a wheel,’ with references selected from the above.
The Collection of Ancient Marbles at Leeds
Authors: Hicks E. L. 
Published: May 2006

The collection of antiquities which forms the subject of this paper was presented in the year 1863—4 to the Museum of the Leeds Philosophical Society by the Rev. John Gott, D.D., then Vicar of Leeds and now Dean of Worcester. He tells me that it came into his hands in the following way. Mr. Benjamin Gott, elder brother of the Dean's father, made a tour in Greece about the year 1815, in the company of an intimate friend, Mr. Rawson. They visited Smyrna, and returned through the islands to Athens, purchasing, in the course of their travels, a number of ancient marbles. Mr. Benjamin Gott died of fever at the Piraeus, and was buried at Athens in the Theseium. Many years afterwards, when an English cemetery was opened at Athens, his body, with two others, was removed from the temple to this more fitting resting-place.Upon Mr. B. Gott's death, the marbles passed into the possession of his fellow-traveller Mr. Rawson, in whose house at Halifax they remained for years. Here six of the inscriptions were copied and sent to Böckh for insertion in the Corpus Inscriptionum Graecarum which he was then preparing.
Inscriptions from Western Cilicia
Authors: Hicks E. L. 
Published: May 2006

There is little danger of any reader nowadays sharing the sentiments of the Pseudo-Aristotle which I have placed at the head of this paper, or of being other than grateful to Mr. Bent for the remarkable discoveries made by him in Cilicia last year. Of the inscriptions which he brought home, either in copies or in squeezes, I have already published those from Eastern Cilicia in the last number of this Journal. Those that here follow are from Cilicia Tracheia. Shortly after Mr. Bent had been through these regions, Mr. Ramsay in company with Messrs. Hogarth and Headlam passed through the upper part of the Olban district, and made an excursion down to the coast expressly to re-copy the long temple-inscription, No. 27 infra. The heat of the lowlands prevented their doing more. They have rendered me all the help they could in editing these documents; several of them are from copies made only by Mr. Ramsay, and the long list of names from the temple over the Corycian Cave is here given from the careful copy of Mr. Ramsay and Mr. Hogarth.Since I began to prepare these inscriptions for the Journal, Mr. Ramsay's remarkable work has appeared on The Historical Geography of Asia Minor. This makes it unnecessary for me to preface these documents (as I had intended to do) with a sketch of the history of Western Cilicia.
Kylix with Exploits of Theseus
Authors: Smith Cecil 
Published: May 2006

The vase from which the designs on Plate X. are copied is a Kylix, or shallow two-handled cup, 5 inches high by 12¾ inches in diameter. It was acquired by the British Museum in 1850, together with other objects included in the sale of the collection of Dr. Emil Braun, who had procured it from the dealer Basseggio: in the sale catalogue it is stated to have been found at Vulci.Notices of this vase have appeared in various works from time to time; Dr. Braun himself exhibited it at the Roman Instituto (Bulletino di Corr. Archeol. 1846, p. 106); Gerhard, in the Archäol. Zeitung for 1846, p. 289, described it briefly; and it is included in the Catalogue of Vases in the British Museum, No. 824*. In publishing for the first time, so far as I am aware, an engraving of this magnificent vase, it may be worth while to add a more detailed description than has hitherto appeared.
Statuette of Pallas from Cyprus
Authors: Gardner Percy 
Published: May 2006

Among the objects recently acquired by the British Museum is a beautiful terra-cotta from a grave at Salamis in the Island of Cyprus, of which I give a representation on Plate XVI. The figure is that of a goddess who wears a long chiton with diploïs, and a himation over her back and arms. Long tresses fall over her shoulders; on her head is apparently a stephane, though it may be intended rather for a taenia or band; in her ears are round earrings. Her right hand is passed into the interior of a crested Corinthian helmet, her left hand rests on the edge of a round shield. Her left foot is slightly drawn back, and the leg bent.The figure is 7¼ inches in height, and stands on a square pedestal ¾ of an inch high. The back is quite unworked, and in the midst of it is the usual round hole, made to facilitate the baking. Slight traces of red colour appear on the hair of the goddess and the crest of the helmet, and we may observe on the lower part of the drapery some of the white ground-mixture with which terra-cotta figures were covered as a basis for colouring.
On an Unedited Rhodian Inscription
Authors: Newton C. T. 
Published: May 2006

I found this inscription in the ruins of a church called Agia Irenè, about a quarter of an hour's distance from the village of Apolakkia in Rhodes. This village is situated near the sea on the south-west side of the island (see my Travels and Discoveries, i., p. 198).This inscription contains part of two decrees, of which the first was passed by the κοινόν of the Euthalidai. The upper part of the stone being wanting, we only know the latter part of this first decree, from which we learn that a crown had been voted by the κοινόν to Sosikrates, son of Kleonymos, a Netteian, and that this honour was to be publicly proclaimed in the usual manner. We learn further that it was necessary that this decree should be confirmed by a Boulè, ‘senate,’ and Demos, ‘popular assembly,’ to the control of which the Euthalidai were subject.
The Imperial German Archaeological Institute
Authors: Michaelis Ad. 
Published: May 2006

Few English scholars have an exact knowledge of the history, the constitution, and the labours of the German Archaeological Institute, although the existing science of classical archaeology may be roughly said to be a creation of that Institute. So when, some months ago, an authoritative paper by Professor Michaelis of Strassburg, a member of the Central Direction, appeared in thePreussische Jahrbücher, supplying exactly such information on these matters as should be current among us, the Editors of this Journal thought that the opportunity thus offered was one of which advantage should be taken. Accordingly permission was obtained from Professor Michaelis and the Editors of theJahrbücherto publish in these pages a translation of the article. The translation was undertaken by Miss Alice Gardner; and Professor Michaelis has himself made some additions to the text to fit it more completely for an English audience. [ED.]Scientific institutions, which take their functions seriously, live a silent life. This is a result of the very nature of scientific work, which in most points of its manifold occupations cannot appeal to a wide public. Only in case of especially important discoveries, or of conspicuous performances, and on festal occasions do such institutions step out of their quiet round of work into public light, and demand the sympathy of wider circles.
The Temple of Apollo at Delphi
Authors: Middleton J. Henry 
Published: May 2006

In many respects Delphi and its varied cults possess an interest which is not to be rivalled by that of any other Hellenic site. The lofty precipices, the dark deeply-cleft ravines, the mysterious caves, and the bubbling springs of pure water, combine to give the place a romantic charm and a fearfulness of aspect which no description can adequately depict.Again Delphi stands alone in the catholic multiplicity of the different cults which were there combined.In primitive times it was the awfulness of Nature which impressed itself on the imaginations of the inhabitants.In an early stage of development the mind of man tends to gloomy forms of religion: his ignorance and comparative helplessness tend to fill his brain with spiritual terrors and forebodings. Thus at Delphi the primitive worship was that of the gloomy Earth and her children, the chasm-rending Poseidon, and the Chthonian Dionysus, who, like Osiris, was the victim of the evil powers of Nature. It was not till later times that the bright Phoebus Apollo came to Delphi to slay the earth-born Python, just as the rising sun dissipates the shadows in the depths of the Delphian ravines, or as in the Indian legend the god Indra kills with his bright arrows the great serpent Ahi—symbol of the black thunder-cloud.
On a Phoenician Vase found in Cyprus
Authors: Richter Max Ohnefalsch 
Published: May 2006

The vase of which I here publish representations is barrel-shaped with round ends, and has at each end protuberances in the form of nipples. There is a small raised ring round the neck. The mouth is funnel-shaped, with edges slightly overlapping. The dimensions are as follows:—Circumference over nipples 2 ft. 7⅝ in. Circumference of barrel 2 ft. 1 in. Height of neck 3½ in. Total height of jar 1 ft. ⅛ in. The vase was bought at Larnaca, and probably found near that place.The vessel is of a purely Phoenician model, though not necessarily of pre-Hellenic times, of a kind occurring not only in earlier and later specimens made by the Phoenician race in Cyprus, but also in pottery manufactured by other races in places in the island where their influence predominated. The clay used in the composition of the jar is of a darkish cream colour, and has evidently been very carefully washed and prepared.
Notes on Amasis and Ionic Black-figured Pottery
Authors: Karo George 
Published: May 2006

Among the artists who have signed Attic black-figured vases perhaps the most singular and interesting personality is the potter and painter Amasis. He is interesting both as one of the masters of that delicate decorative work, which gives b.f. vases their artistic value, and through the curious contradictions which can be traced in his style. Only seven vases bearing his signature are known up till now, yet each shows characteristic peculiarities of shape, decoration, or style, which one would seek for in vain among the mass of contemporary Attic pottery.No artist has surpassed Amasis in easy mastery and accuracy of drawing, or in the painstaking, delicate treatment of detail; yet his figures are often rigid and affected, his choice of subjects monotonous and limited. The technique and style of his vases, the alphabet and dialect of their inscriptions prove that he worked in Athens; yet both his numerous peculiarities of style and his name seem to denote a foreign origin.It is but natural that so peculiar and interesting an artist should have excited curiosity to trace his origin and influence, and the wish to enrich the scanty stock of his work which we possess, by unsigned vases that may be attributed to him.
Some Observations on the Persian Wars. 2. The Campaign of Xerxes
Authors: Munro J. A. R. 
Published: May 2006

The defeat at Marathon made it doubly necessary for the Persian government to undertake the subjugation of the Greeks across the sea. If there was ever to be peace on the Aegean that ‘Majuba’ must be ‘wiped off the slate.’This time there was to be no mistake. The expedition was long and carefully prepared, and was planned on an enormous scale. The number of Xerxes' host cannot indeed be demonstrated, but it may be estimated with some probability, and the historian is bound to attempt an estimate. No sane critic could accept the millions of Herodotus. Nor would many now be found to admit the 700,000 or 800,000 given with or without garniture by Isocrates, Ctesias, and the later authors who mostly depend upon Ephorus. These figures seem to have been deduced from Herodotus. In iv. 87, the land forces led by Darius against the Scyths are said to have numbered 700,000, and it is implied that they were the full levy of the entire empire. In viii. 100 and 113, Mardonius is to be left with 300,000, while Xerxes goes home with the larger part of the army (cf. Thuc. i. 73). In vii. 20, Xerxes' host is larger than that of Darius or any other on record.
Archaeology in Greece, 1895–6. I. General
Authors: Pharmakovsky B. 
Published: May 2006

The past year has not been productive of any momentous discovery, excepting only the bronze statue at Delphi, which will be described more fully in its own place; but a great amount of useful work has been done in various directions, and, indeed, the great variety of what has been achieved may be regarded as the characteristic feature of the year.In Athens, the excavations in the neighbourhood of the Pnyx and the Areopagus have reached their third season. In the later months of 1894 the entire shrine which Dörpfeld identifies as that of Dionysos was laid bare, with its temple, altar, and wine-press. The archaic structure seems to have been in existence down to late Greek times, when its site was covered by a building which is identified by an inscription as the assembly house of the Iobacchi. From the different methods of construction which can be traced in the walls, it would seem that this building must have stood for a long period; the base of the altar, belonging to the earlier stage, is fairly well preserved; it consisted of a table supported on four slender columns, replaced later by four larger supports; at one side on the step are sinkings for two stelæ; Dörpfeld points out that according to Demosthenes (?) (Neaera, 76) the oath which the Gerairai had to swear at the sacred marriage of the Basilinna in the Anthesteria was inscribed on a stelè set up an expression which suits the proposed identification.
Antique Rings Pierced With Gold Nails
Authors: Marshall F. H. 
Published: May 2006

Among the silver rings in the Department of Greek and Roman Antiquities in the British Museum are seven which have a stud or nail of gold driven through the bezel. The intaglio designs on these rings are as follows:—(1) Two sphinxes confronted. (2) Ox-head and bird placed opposite one another on oblong bezel. (3) Recumbent lion to r. looking back over its shoulder. Cf. Furtwängler, Besehreibung der geschn. Steine im Antiq., No. 152. These three designs are archaic in style. (4) Woman seated to r., holding out dove on 1. hand. Cf. a coin of Eryx (Gardner, Types of Greek Coins, PI. VI. 3). On the ring a wreath takes the place of the standing Eros. (5) Design similar to last, but in reverse direction; no wreath.The last two rings are of good style, but poor execution (4th—3rd cent. B.C.). (6) Very much worn; a female figure can be made out. (7) A very curious design, which I am unable to explain. A jackal's head surmounts a vaselike object. Before the head is a curved, behind, a straight handle (?).
A Fourth Century Head in Central Museum, Athens
Authors: Benson E. F. 
Published: May 2006

There is among the fourth century works in the Central Museum at Athens a head found at Laurium. It is made of Parian marble but it has been completely discoloured by slag or refuse from the lead mines, and is now quite black. In its present condition it is quite impossible to obtain a satisfactory photograph of it, and the reproduction given of it in the figure is from a cast.It has been published, as far as I am aware, only in M. Kavvadias' catalogue. There it is described as a head of the Lykeian Apollo. This identification rests solely on a passage of Lucian, who mentions a statue of the Lykeian Apollo in the gymnasium at Athens.He says of it ( 7)—It will be seen from a glance at the photograph that the grounds for this identification are very slender. The left hand with the bow does not exist, and the only reason for supposing therefore that this is a head of the Lykeian Apollo consists in the fact that the right hand of the statue rests on the head. This in itself seems insufficient and, among other reasons, it is I think rendered impossible by the phrase For the hand is not idly resting, it is not a tired hand; the posture of the fingers is firm and energetic.
Theseus, Sinis, and the Isthmian Games
Authors: Tillyard E. M. W. 
Published: May 2006

There are in the Hope Collection two vases, which may help towards an explanation of the well-known myth of Theseus and Sinis. They are both known from publications of about a hundred years back, but have for a long period been lost sight of. By the kindness of the owners I am able to bring them once more to light.The scene from the side of one of them was published by Millin in his Peintures de Vases Antiques. It shows in the middle a tree growing from a small rise of ground. To the left of it stands Sinis, naked and bearded. He has pulled down a branch. To the right is Theseus, a young man in travelling costume, wearing a sword and carrying two spears. He has pulled down a larger branch. On the extreme left is a draped bearded man holding a sceptre. Millin writes, ‘le vase est aujourd'hui en Angleterre: il appartient à M. Edouard.’ By ‘M. Edouard’ he must mean J. Edwards, whose collection was dispersed in 1815, when the vase probably came directly into the hands of Thomas Hope. Millin's drawing is so incorrect and his description so scanty (he does not even indicate the shape) that a republication is necessary.
Pylos and Sphacteria
Authors: Burrows Ronald M. 
Published: May 2006

Grateful as we must all be to Mr. Compton and Mr. Awdry for their adventurous climb, which to my mind has finally settled the path that the Messenians took to reach the foot of the gorge or gully, we have probably been puzzled by some of their incidental remarks. I feel the less reluctance in commenting on them that most of my criticisms would, by their kindness, have been embodied in the article itself, had I not been absent in Greece at the time it was being written.In the first place what they call the ‘notch’ is what Dr. Grundy and I both call the ‘hollow.’ The word hollow was kept by Messrs. Lindsay, Bosanquet, and Crowfoot, and there is no reason, I understand, for the change except inadvertence. It is more serious, however, that the part played by this hollow in the last struggle of the Spartans is misconceived.
An Inscription from Side
Authors: Vincent Hugues 
Published: May 2006

The Editors have received the following note from R. P. Hugues Vincent, of the École biblique et archéologique St. Étienne, Jerusalem:—L'inscription grecque de Side est du plus haut intérêt archéologique; cela n'a pas échappé à M. v. Buren. Son commentaire très concis appellerait beaucoup de développements et peut-être ici ou là une réserve—par exemple dans l'équivalence ϕροντιστής = ἀρχισυνάγωγος. Ce n'est pas le lieu d'aborder cela ici. Je veux seulement vous signaler une hypothèse séduisante pour restituer le début du texte qui sera ainsi tout à fait complet.