Important examples of $\Pi^0_1$ classes of functions $f \in {}^\omega\omega$ are the classes of sets (elements of ω 2) which separate a given pair of disjoint r.e. sets: ${\mathsf S}_2(A_0, A_1) := \{f \in{}^\omega2 : (\forall i < 2)(\forall x \in A_i)f(x) \neq i\}$ . A wider class consists of the classes of functions f ∈ ω k which in a generalized sense separate a k-tuple of r.e. sets (not necessarily pairwise disjoint) for each k ∈ ω: ${\mathsf S}_k(A_0,\ldots,A_k-1) := (...) \{f \in {}^\omega k : (\forall i < k) (\forall x \in A_i) f(x) \neq i\}$ . We study the structure of the Medvedev degrees of such classes and show that the set of degrees realized depends strongly on both k and the extent to which the r.e. sets intersect. Let ${\mathcal S}^m_k$ denote the Medvedev degrees of those ${\mathsf S}_k(A_0,\ldots,A_{k-1})$ such that no m + 1 sets among A 0,...,A k-1 have a nonempty intersection. It is shown that each ${\mathcal S}^m_k$ is an upper semi-lattice but not a lattice. The degree of the set of k-ary diagonally nonrecursive functions $\mathsf{DNR}_k$ is the greatest element of ${\mathcal S}^1_k$ . If 2 ≤ l < k, then 0 M is the only degree in ${\mathcal S}^1_l$ which is below a member of ${\mathcal S}^1_k$ . Each ${\mathcal S}^m_k$ is densely ordered and has the splitting property and the same holds for the lattice ${\mathcal L}^m_k$ it generates. The elements of ${\mathcal S}^m_k$ are exactly the joins of elements of ${\mathcal S}^1_i$ for $\lceil{k \over m}\rceil \leq i \leq k$. (shrink)

Few years pass without an attempt to interpret Theocritus, Idyll 7. The poem's narrative and descriptive skill, dramatic subtlety and felicity of language are mercifully more than adequate to survive these scholarly onslaughts, so I have less hesitation in offering my own interpretation. The poem's chief problems seem to me to arise from uncertainty as to: Who is the narrator, and why are we kept waiting until line 21 before we are told that he is called Simichidas? Who, or what (...) sort of man, is the goatherd Lycidas, whom he encounters on his way from town to the harvest festival? Answers to these questions fundamentally affect our interpretation of their exchange of songs, which occupies almost half the idyll, and of Lycidas' gift of his stick to Simichidas; and these interpretations will go far towards interpreting the poem as a whole. (shrink)

post hos elefantorum fulgentium formidandam speciem et truculentos hiatus uix mentes pauidae perferebant; ad quorum stridorem odoremque et insuetum aspectum magis equi terrebantur. COKNELISSEN, Mnemosyne, xiv , 280, comments: ‘Non intellego fulgentium. Minime audiendus est Wagnerus, qui fulgentes elephantes dictos esse contendit ob cutem glabram. Corrigendum puto ingentium. Porro non satis intellego quomodo hiatus elefantorum militibus pauorem incutere potuerit. Wagnerus, qui omnia con-coquere solet, interpretatur proboscidas. Nescio an scripserit A. barritus.’.