bluuebunny/crossref_metadata_2025_split huggingface dataset:
Address at the Princeton University Bicentennial Conference on Problems of Mathematics (December 17–19, 1946), By Alfred Tarski
Authors: Sinaceur Hourya 
Published: May 2006

AbstractThis article presents Tarski's Address at the Princeton Bicentennial Conference on Problems of Mathematics, together with a separate summary. Two accounts of the discussion which followed are also included. The central topic of the Address and of the discussion is decision problems. The introductory note gives information about the Conference, about the background of the subjects discussed in the Address, and about subsequent developments to these subjects.
Inner Models and Large Cardinals
Authors: Jensen Ronald 
Published: May 2006

In this paper, we sketch the development
of two important themes of modern set theory, both
of which can be regarded as growing out of work of
Kurt Gödel. We begin with a review of some basic
concepts and conventions of set theory.
§0. The ordinal
numbers were Georg Cantor's deepest contribution
to mathematics. After the natural numbers 0, 1, …,
n, … comes the first
infinite ordinal number ω, followed by ω + 1, ω +
2, …, ω + ω, … and so forth. ω is the first
limit ordinal as it is
neither 0 nor a successor ordinal. We follow the
von Neumann convention, according to which each
ordinal number α is identified with the set {ν ∣ ν
α} of its predecessors. The ∈ relation on ordinals
thus coincides with <. We have 0 = ∅ and α + 1
= α ∪ {α}. According to the usual set-theoretic
conventions, ω is identified with the first
infinite cardinal ℵ0,
similarly for the first uncountable ordinal number
ω1 and the first uncountable
cardinal number ℵ1, etc. We
thus arrive at the following picture:

The von Neumann
hierarchy divides the class
V of all sets into a
hierarchy of sets
Vα
indexed by the ordinal numbers. The recursive
definition reads:
(where } is
the power set of
x);
Vλ
=
∪v<λVv
for limit ordinals λ. We can represent this
hierarchy by the following picture.
The Mathematical Import of Zermelo's Well-Ordering Theorem
Authors: Kanamori Akihiro 
Published: May 2006

Set theory, it has been contended, developed from its beginnings through a progression ofmathematicalmoves, despite being intertwined with pronounced metaphysical attitudes and exaggerated foundational claims that have been held on its behalf. In this paper, the seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject. The motif is foreshadowed in Cantor's diagonal proof, and emerges in the interstices of the inclusion vs. membership distinction, a distinction only clarified at the turn of this century, remarkable though this may seem. Russell runs with this distinction, but is quickly caught on the horns of his well-known paradox, an early expression of our motif. The motif becomes fully manifest through the study of functionsof the power set of a set into the set in the fundamental work of Zermelo on set theory. His first proof in 1904 of his Well-Ordering Theoremis a central articulation containing much of what would become familiar in the subsequent development of set theory. Afterwards, the motif is cast by Kuratowski as a fixed point theorem, one subsequently abstracted to partial orders by Bourbaki in connection with Zorn's Lemma. Migrating beyond set theory, that generalization becomes cited as the strongest of fixed point theorems useful in computer science.Section 1 describes the emergence of our guiding motif as a line of development from Cantor's diagonal proof to Russell's Paradox, fueled by the clarification of the inclusion vs. membership distinction. Section 2 engages the motif as fully participating in Zermelo's work on the Well-Ordering Theorem and as newly informing on Cantor's basic result that there is no bijection. Then Section 3 describes in connection with Zorn's Lemma the transformation of the motif into an abstract fixed point theorem, one accorded significance in computer science.
On the Decision Problem for Two-Variable First-Order Logic
Authors: Grädel Erich , Kolaitis Phokion G. , Vardi Moshe Y. 
Published: May 2006

AbstractWe identify the computational complexity of the satisfiability problem for FO2, the fragment of first-order logic consisting of all relational first-order sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity of its decision problem has not been pinpointed so far. In 1975 Mortimer proved that FO2 has the finite-model property, which means that if an FO2-sentence is satisiable, then it has a finite model. Moreover, Mortimer showed that every satisfiable FO2-sentence has a model whose size is at most doubly exponential in the size of the sentence. In this paper, we improve Mortimer's bound by one exponential and show that every satisfiable FO2-sentence has a model whose size is at most exponential in the size of the sentence. As a consequence, we establish that the satisfiability problem for FO2 is NEXPTIME-complete.
The Graeco-Roman Civilisation in Pisidia
Authors: Ramsay W. M. 
Published: May 2006

1. On June 3, 1882, while travelling from Apollonia to Antioch of Pisidia, we observed a long inscription in a cemetery by the roadside, about eleven or twelve miles west of the latter town, and close to the village of Gondáne. It was engraved on a pillar of peculiar shape, commonly used in Roman and Byzantine times: a horizontal section of the column would give the annexed figure.A short inspection showed that the inscription was important, and Sir C. Wilson delayed the march for a day to allow me to copy it. I was exceedingly anxious to get an impression, but a strong and bitterly cold north wind, accompanied by frequent heavy showers, frustrated our attempts. At last, by laying my coat over the impression-paper on the stone, I got a squeeze of a small part. The inscription has been engraved by an unskilful workman: the lines are very uneven, the letters are unequal in size and various in form, sometimes deeply and clearly cut, sometimes merely scratched, ligatures are frequent, and often three, or even four, letters are united. In some cases it was impossible to tell, except from the meaning, whether a group of letters belonged to one line or another. In the heavy rain the only way of copying the inscription was to learn half a line by heart, and get into some shelter where I could write it out in my notebook. In this way I made a complete copy during the day: at night I wrote out lists of the proper names, compared the different forms together, and made a note of the places where difficulties struck me. Next morning the rest of the party went on to Antioch: I waited behind, revised the whole of the inscription, and carefully observed every difficulty that I had noted. A few other difficulties have occurred to me in subsequent study of the inscription; but in the great majority of cases where I remark on an uncertainty, the difficulty was distinctly present in my mind when comparing the copy with the stone.
Views of Athens in the year 1687
Authors: Waldstein Charles 
Published: May 2006

Since such works as Beulé's L'Acropole, d'Athènes, the Count De Laborde's Athènes au xv.e, xvi.e, et xvii.eSiècles, and Michaelis's Parthenon have appeared, the history of the Acropolis and its buildings has been made widely known, or at least the ascertainment of exact information has been made easy for all interested in these subjects. The more complete the list of records, the more importance do we attach to any new document referring directly to the Acropolis or the Parthenon. The two drawings in the library of the late Sir Thomas Phillipps at Thirlstane House, Cheltenham, here published, give views of the Acropolis in 1687.The main points in the history of the Parthenon (for this ever remains the centre of interest on the Acropolis of Athens), are the following: After its completion in 438 B.C. it appears to have remained in its original condition until it was turned into a Christian church about the middle of the fifth century or the middle of the sixth, and by peculiar persistency of its original dedication to the virgin goddess of wisdom, it appears to have been at first converted into a church of St. Sophia and then of the Virgin Mary. The alterations made chiefly affected the interior of the temple.
On the Fragment of Proclus' Abstract of the Epic Cycle contained in the Codex Venetus of the Iliad
Authors: Monro D. B. 
Published: May 2006

The document which is the subject of the following paper has the interest of being the only copy of the only direct record of a whole period of Greek literature—the period, namely, of the poets who carried on the traditions of Homeric art in the eighth and seventh centuries B.C. It is a fragment in a double sense: first because it is a mere extract, and secondly because the pages on which it is preserved are themselves in a fragmentary condition. It professes to be derived from a certain χρηστομάθεια γραμματική—a kind of primer or résumé of Greek literature—the work of a grammarian named Proclus; and contains, with other matter, part of his account of the so-called ‘Epic Cycle.”Regarding Proclus himself nothing is certain, except that he is not Proclus Diadochus, the Platonic philosopher of the fifth century. According to Welcker's probable conjecture, he is to be identified with Eutychius Proclus of Sicca, instructor of the emperor M. Antoninus
Inscriptions copied by Cockerell in Greece.—II
Authors: Gardner E. A. 
Published: May 2006

In the earlier number of the present volume (p. 143 sqq.) I gave some account of a MS. collection of inscriptions made by C. R. Cockerell in 1810–1814, and also gave copies of all those from the mainland of Greece, which appeared to be hitherto unpublished. The present paper will cover the rest of that collection, which is mostly derived from Asia Minor.I add a complete list of the remaining contents of Cockerellľs volumes. Those unpublished are reproduced below; in the case of all those previously edited, a collation with the published copy has been made and kept, and I should be very glad to show these collations to any one interested in the matter.
Inscriptions from Eastern Cilicia
Authors: Hicks E. L. 
Published: May 2006

Kars-Bazaar is about four hours from Boudroum; in its situation it agrees with Flaviopolis, standing on a branch of the river Pyramus, at the foot of the mountains. Unfortunately none of the inscriptions reveal the name of the site.‘A very handsome tessellated pavement in a cottage, with an elaborate pattern, in the centre of which is the following legend.’ Copied by Mr. Bent.Probably from the floor of an early church. Dedicated by the guild of fullers. It is interesting to see these trade-guilds, so common under the Empire in Asia Minor, passing unchanged into the Christian Church. For συνέργιον = συνεργασία, see C. I. G. 4346 and Addenda, p. 1163 (from Side).
Fourteenth-Century Tachygraphy
Authors: Allen T. W. 
Published: May 2006

The Vatican MS. numbered Regina 181, written in 1364 and containing the medical works of Actuarius, has at various parts of it several more or less continuous pieces of tachygraphy that, considering the late date of the MS. and the character of the tachygraphical system itself, are very remarkable. I was made aware of the existence of these specimens of tachygraphy from Signor Enrico Stevenson's recent catalogue of the Queen of Sweden and Pio II. collection (Rome 1888), and on a recent visit to Rome I had photographs taken of two of the principal passages where tachygraphy is employed: these are reproduced here.The MS. itself is a paper book, measuring 8½ inches by 5, written according to the subscription in 1364: for a fuller description and a list of the contents I may refer to Signor Stevenson. The tachygraphical matter in the book falls into three divisions: first, certain passages in the text, where, departing from his ordinary usage, the scribe suddenly as it were drops into shorthand; secondly, a formal table of tachygraphical and other signs, with their interpretations at the end of the book; and lastly, two notes of considerable length, and of somewhat uncertain meaning, which are written on either side of an empty page between the table of contents and the text.
The Theatre at Megalopolis
Authors: Gardner E. A. , Loring William , Richards G. C. , Woodhouse W. J. 
Published: May 2006

In view of the great interest which has been expressed in the Theatre at Megalopolis, now in course of excavation by members of the British School at Athens, and of its real importance in connection with the question of the Greek Stage, it has been determined to publish, provisionally, a plan and section of it, without waiting for the completion of the work. The excavation will, it is hoped, be finished in the spring: and a full account of our results, with the necessary plans and illustrations, will be published in a future number of this Journal. For the present, therefore, a very few words of explanation must suffice.The following is an explanation of the woodcuts, made from Mr. Loring's drawings:—
Notes on the Antiquities of Mykenae
Authors: Petrie W. M. Flinders 
Published: May 2006

When a new field of view was opened to us some years ago by Schliemann's unearthing of Mykenae, there were no sufficient data already known to enable us to judge of the age of the civilization there presented to us. Since then the discovery of many other pre-Hellenic tombs in Greece, and the unexpected links which I have found in Egypt, afford some basis for an approximate chronology. We will therefore consider here (l) the comparisons between the objects found in the six tombs in the circle at Mykenae, and others found in Egypt, (2) the relation of these to other pre-Hellenic tombs, (3) the artistic and climatic data bearing on the Mykenaean civilization. I cannot profess these notes to be exhaustive; they are merely what occurs to a bystander who is more familiar with Egyptian archaeology; and many of the facts I am indebted to Mr. Ernest Gardner and Mr. Walter Leaf for pointing out to me, while examining the collections at Athens.Taking the graves in the order of their numbers (as adopted in the Museum and by Furtwaengler), we find in grave I. a group of glass beads which have been greatly changed by moisture: the original colour is seen where the outer scale is broken away, it was a clear prussian blue, decomposing to white on the surface.
A Journey in Cilicia Tracheia
Authors: Bent J. Theodore 
Published: May 2006

The district which forms the subject of the following remarks is that which we know from Strabo, as well as from numismatic evidence, to have formed the kingdom of Olba, ruled over in ancient times by a family of priest-kings, priests of Jove, dynasts of Olba, and toparchs of Lalassis and Kennatis. Having made a careful exploration of this district, and collected therein the inscriptions which are to follow, I propose to treat the subject-matter under four distinct heads, into which the ground traversed naturally divides itself:—First, the ruins of the three great coast towns between the mouth of the Lamas gorge and the plain of Selefkeh, namely Augusta-Sebaste or Elaeussa, Corycos, and Pseudo-Corasion.Secondly, the first plateau above the sea, studded with ruined towers and villages, and chiefly remarkable for the three great caves or depressions in the ground, one dedicated to the Corycian Jove, a second to the Olban Jove, and a third alluded to only by Pomponius Mela as Typhoneus.
Homeric and Hellenic Ilium
Authors: Jebb R. C. 
Published: May 2006

Dr. Schliemann has proved that Hissarlik was a seat of human habitation from a prehistoric age. This has not been proved for any other place which could claim to be the site of Homeric Troy. Assuming that ‘the tale of Troy’ is founded on a central fact—i.e., that a very old town, placed as the Iliad roughly indicates, was once besieged and taken—the claim of Hissarlik to be the site of that town is now both definite and unique. Thus far, Dr. Schliemann's argument is unanswerable. It is not my purpose to discuss here the further questions which arise as to the relation of his discoveries to places or objects described in the Iliad. The subject of which I would speak is historical rather than strictly archæological, yet one which, within certain limits, has a distinct bearing on Dr. Schliemann's results.What was the belief of the ancient Greeks as to the site of Homeric Troy? And, in particular, how did they generally regard the claim of the Greek Ilium (at Hissarlik) to be considered as occupying the Homeric site?
Imperial Cuirass-Ornamentation, and a Torso of Hadrian in the British Museum
Authors: Wroth Warwick 
Published: May 2006

In the last volume of the Journal of Hellenic Studies (vi. pp. 378–380) Prof. Newton has commented at length on some remarks made by me in the same volume (vi. pp. 199—201) on the torso of an imperial statue found at Cyrene and now in the British Museum. Before considering Mr. Newton's paper in detail I may be permitted to say a few words on the subject of cuirass-ornamentation in general.In his Winckelmanns-fest-program for 1868, Dr. Hübner referred to the want of a classified list of ornamented cuirasses of emperors. No one has, at present, attempted to compile such a list, which would, practically, have to take the form of a complete monograph on statuae thoracatae, in which the restorations, style, material, pose, and attribution of each figure would have to be carefully studied. To carry out this work it would be necessary to make a personal examination of a large number of statues which have not hitherto been critically described, and which have suffered greatly at the hands of restorers. A difficulty which specially complicates the study of this class of monuments would also have to be borne in mind— namely, that in many cases the body of imperial statues appears to have been originally made apart from the head.
Nikè Sacrificing a Bull
Authors: Smith Cecil 
Published: May 2006

The group of Nikè βουθυτοῦσα is one which is already so well known among works of ancient art, that in adducing further instances of this type we cannot hope to bring forward much that adds to our previous knowledge of the subject. It is, however, just one of those cases which, from the very frequency of its recurrence in ancient art, has a special claim upon our attention; a motive which, starting as it doubtless does, from a great Greek original, continues favourite down to late Roman times, is worthy of study in the phases of development which different material and different periods bring about, and therefore I think no apology is needed for introducing the fresh examples of it now before us.The starting point, the Haupttypus so far as we know, of this motive, is of course the small fragment which remains to prove that it existed in the reliefs on the balustrade of the temple of Athena Nikè at Athens. In his admirable monograph on these sculptures, published in 1869, Kekulé contented himself with a brief description of this fragment, without being able to identify the original motive of the group from which it came, or its position on the frieze.
Discoveries in Asia Minor
Authors: Bent J. Theodore 
Published: May 2006

At the commencement of our cruise along the south coast of Asia Minor we first touched at Capo Krio and examined closely the tombs in the neighbourhood of Cnidos, which were constructed on rising ground about two miles to the east of the ancient town. Most of them were about 20 ft. square; some built entirely of polygonal masonry, others with the sides in polygonal masonry and the fronts in square-cut stones. Along this front ran a narrow line of square-cut stones on which in most cases traces of inscriptions appeared, but owing to the nature of the stone almost all the letters were defaced with the exception of the following:…. ΤΑΣΣΑΣΕΡΜ. ΑΣ. …In the upper chambers were many grave altars and memorial tablets; in two graves we found altars with snakes represented as coiled around them, and in another an altar with the ordinary bull's head and garland decoration, bearing the inscription ΟΔΑΜΟΣ (ἀνέθηκεν).Proceeding along Capo Krio to the point where the land contracts into a narrow isthmus we found traces of other tombs which have lately been exposed to view by the washing away of the soil by a winter's flood. In these tombs have been found many small marble figures similar to those I found at Antiparos and described in this Journal (vol. v. p. 50). One represents a figure seated in a chair playing a harp similar to that in the Museum at Athens, which was found at Amorgos, another is of a female figure with a crescent on her head similar to one which I have seen, and which was discovered in the island of Tenos.
A Study of Phrygian Art.–I
Authors: Ramsay W. M. 
Published: May 2006

A brief introductory statement of the historical views to which I have been led by a study of the Phrygian monuments will make the following pages clearer, and will enable the reader to criticise the whole with greater advantage. I can hardly hope to have reached the truth in regard to this difficult subject; but it is so closely connected with many disputed points in early Greek history that I have thought it best to carry out my view to its logical conclusions and state the whole in brief and precise terms. This will place the reader on his guard from the beginning, and if it leads him to exercise unsparing criticism, I shall have attained my object.1. The Phrygians are a European race, who entered Asia Minor across the Hellespont: the unanimous Greek tradition to this effect (which at one time I regarded as probably a reversal of the truth) is confirmed by longer study of the country and the monuments.2. The Phrygians and the Carians were two very closely kindred tribes, nearly related to some of the Greek races, who established themselves in the countries which bear their name as a conquering and ruling caste amid a more numerous alien population: they were mail clad warriors whose armour gave them great advantage over opponents equipped in the slighter oriental fashion. Greek tradition associated various improvements in the style of armour with the Carians, and a relief published below (fig. 9) shows two Phrygian warriors armed quite in the Carian style.
Note on the Inscription from Priene
Authors: Hicks E. L. 
Published: May 2006

I have been favoured with a letter from M. Haussoullier, Professor of Greek Antiquities at Bordeaux, respecting the Prienian decree which I published in the last number of this Journal from the MS. copy of Mr. Murray. M. Haussoullier, whose valuable contributions to Greek epigraphy are well-known, especially to readers of the Bulletin de Correspondance Hellénique, tells me that he visited Prienè in 1879 and took an impression and copy of this same inscription. He has very kindly communicated to me the readings in which his impression differs from Mr. Murray's MS. The comparison proves the general accuracy of Mr. Murray's copy.Line 9.—Murray τὸν χρόνον: Haussoullier τὸγ χρόνον.Line 19.—Murray ὅπως δαμη, from which I restored ὅπως δ[ε]μή: Haussoullier ὅπως δ'ἀ… only.
Coin-types of some Kilikian Cities
Authors: Imhoof-Blumer F. 
Published: May 2006

The era of the city begins in the autumn of 47 B.C. Hence this coin, which is struck in high relief, dates from the second year of the reign of Trajan (autumn 98–99 A.D.). The head is not a likeness. The inscription on the reverse identifies the goddess represented with the Ἐκκλησία of the Aigeaians, a personification which has not hitherto, as far as I know, occurred on coins.2. 26. Bust of the Caesar, laureate, to right, wearing cuirass and draped.Rev. 1. in the field. Tyche seated to left, wearing a turreted crown and veil. In her right, a small temple represented in profile, with a statue under the arch of the façade and an eagle on the pediment. At the feet of the goddess a goat lying to left, its head reverted.