Tarski [5] showed that for any set X, its set w(X) of well-orderable subsets has cardinality strictly greater than that of X, even in the absence of the axiom of choice. We construct a Fraenkel-Mostowski model in which there is an infinite strictly descending sequence under the relation |w (X)| = |Y|. This contrasts with the corresponding situation for power sets, where use of Hartogs' ℵ-function easily establishes that there can be no infinite descending sequence under the relation |P(X)| = (...) |Y|. (shrink)

The Problems, which occupy pp. 859-967 of the Berlin Aristotle, have probably been less read and studied than any other treatise in the Aristotelian Corpus; they contain, however, a vast quantity of interesting information on a great variety of subjects, and an enquiry into their composition may be not without interest.

In dit essay keert Forster zich tegen geloof met een grote G: het fundamentalistisch geloof in een religie als de enige bron van waarheid, maar ook het geloof in de macht en het geweld van grote mannen en ideologieën. Hij stelt er zijn eigen geloof met een ‘heel kleine g’ tegenover, een geloof in vrijheid, democratie en individualisme, in de adel van de geest.

ASPECTS OF THE NOVEL is a unique attempt to examine the novel afresh, rejecting the traditional methods of classification by chronology or subject-matter. Forster pares down the novel to its essential elements as he sees them: story, people, plot, fantasy, prophecy, pattern and rhythm. He illustrates each aspect with examples from their greatest exponents, not hesitating as he does so to pass controversial judgement on the works of, among others, Sir Walter Scott, Charles Dickens and Henry James. Full of (...) Forster's renowned wit and perceptiveness, ASPECTS OF THE NOVEL offers a rare insight into the art of fiction from one of our greatest novelists. 'His is a book to encourage dreaming.' Virginia Woolf. (shrink)

We consider the relation between versions of Ramsey’s Theorem and König’s Infinity Lemma, in the absence of the axiom of choice.

We consider the relation between versions of Ramsey’s Theorem and König’s Infinity Lemma, in the absence of the axiom of choice.

While translating the pseudo-Aristotelian Problems for the Oxford translation of Aristotle, I have frequently found it necessary to refer to the Fragments of Theophrastus , which are obviously the source of many of the Problems, in particular in books II., V., XX., XXIV., and XXVI. The condition of the text of both the Problems and the Fragments of Theophrastus leaves much to be desired, but considerable improvements are possible in those passages where the compiler of the Problems is adapting or (...) copying from Theophrastus. (shrink)