From collocations to terms

Collocation as a syntactical and semantic unit, in which one of lexical components is combined with the other distinguished element with the high level of predictability, is in the focus of text researchers. They are studied using the automatic text analysis, compiling general and terminological dictionaries. A large amount of term combinations in scientific texts impels linguists to study conditions that have lead to forming such unities, and also possibilities of their summarization in one-word. The spreading of word combinations with adverbial or adjectival component has become the subject of this paper. A part of them form numerous term families of split nominations with a similar key word. In scientific text the number of terms grows and requires the attention of researchers to the structure of phrases and the possibility of converting them into a stable notion of unity and further shortening them into “words-univerbs” that become some kind of a simple affixed creation with one root: солянокислий гематин – гемін. Others turn into сomposites – consequences: blood corpuscle – білі кров’яні тільця – еритроцити – білокрівці, термофіли, теплолюбні організми, теплолюби. In systems of the automated text analysis it is important to highlight phrases-collocations (constant composition, frequent of repetition of the same meaning) claiming the role of terms. Outlining type of word-combinations according to their structure is relevant. Adjectives and nouns, nouns, nouns and verb word-combinations are best studied nowadays. Resent years three-componental adverbial-and-atributtive-and-substantive terms, that show the importance of fixing in a term some aspects of characteristics of basic component: біологічно активна речовина, морфологічно комунікативно спрямована категорія, морфологічна когнітивно орієнтована категорія, морфологічна формально спрямована категорія.

PSEUDORECURSIVE VARIETIES OF SEMIGROUPS — II

Constructions that yield pseudorecursiveness in [I] (Int. J. Algebra Comput.6 (1996) 457–510) are extended in this article. Finitely based varieties of semigroups with increasingly strict expansions by additional unary operation symbols or individual constants are shown to have the pseudorecursive property: the equational theory is undecidable, but the subsets obtained by bounding the number of distinct variables are all recursive. The most stringent case considered here is the single unary operation or distinguished element. New techniques of stratified reducibility and interpretation via rewriting rules are employed to show the property inherits along a chain of theories. Pure semigroup varieties that are both finitely based and pseudorecursive will be discussed in a later paper.

Ulam's pathological liar game with one half-lie

We introduce a dual game to Ulam's liar game and consider the case of one half-lie. In the original Ulam's game, Paul attempts to isolate a distinguished element by disqualifying all but one ofnpossibilities withqyes-no questions, while the responder Carole is allowed to lie a fixed numberkof times. In the dual game, Paul attempts to prevent disqualification of a distinguished element by “pathological” liar Carole for as long as possible, given that a possibility associated withk+1lies is disqualified. We consider the half-lie variant in which Carole may only lie when the true answer is “no.” We prove the equivalence of the dual game to the problem of covering the discrete hypercube with certain asymmetric sets. We defineA1*(q)for the casek=1to be the minimum numbernsuch that Paul can prevent Carole from disqualifying allnelements inqrounds of questions, and prove thatA1*(q)~2q+1/q.

The Steel hierarchy of ordinal valued Borel mappings

Given well ordered countable sets of the form Λϕ, we consider Borel mappings from Λϕω with countable image inside the ordinals. The ordinals and Λϕω are respectively equipped with the discrete topology and the product of the discrete topology on Λϕ. The Steel well-ordering on such mappings is denned by ϕ ≤ ψ iff there exists a continuous function f such that ϕ(x) ≤ ψof(x) holds for any x ϵ Λϕω. It induces a hierarchy of mappings which we give a complete description of. We provide, for each ordinal α, a mapping whose rank is precisely α in this hierarchy and we also compute the height of the hierarchy restricted to mappings with image bounded by α. These mappings being viewed as partitions of the reals, there is, in most cases, a unique distinguished element of the partition. We analyze the relation between its topological complexity and the rank of the mapping in this hierarchy.

The Coherence Number of 2-Groups

Let G be a finite group. A natural invariant c(G) of G has been defined by W.J. Ralph, as the order (possibly infinite) of a distinguished element of a certain abelian group associated to G. Ralph has shown that c(Zn) = 1 and c(Z2 ⴲ Z2) = 2. In the present paper we show that c(G) is finite whenever G is a dihedral group or a 2-group, and obtain upper bounds for c(G) in these cases.

On models of the elementary theory of (Z, +, 1)

Let T1 be the complete first-order theory of the additive group of the integers with 1 as distinguished element (in symbols, T1 = Th(Z, +, 1)). In this paper we prove that all models of T1 are ℵ0-homogeneous (§2), classify them (and lists of elements in them) up to isomorphism or L∞κ-equivalence (§§3 and 4) and show that they may be as complex as arbitrary sets of real numbers from the point of view of admissible set theory (§5). The results of §§2 and 5 together show that while the Scott heights of all models of T1 are ≤ ω (by ℵ0-homogeneity) their HYP-heights form an unbounded subset of the cardinal .In addition to providing this unusual example of the relation between Scott heights and HYP-heights, the theory T1 has served (using the homogeneity results of §2) as an example for certain combinations of properties that people had looked for in stability theory (see end of §4). In §6 it is shown that not all models of T = Th(Z, +) are ℵ0-homogeneous, so that the availability of the constant for 1 is essential for the result of §2.The two main results of this paper (2.2 and essentially Theorem 5.3) were obtained in the summer of 1979. Later we learnt from Victor Harnik and Julia Knight that T1 is of some interest for stability theory, and were encouraged to write up our proofs.During 1982/3 we improved the proofs and added some results.

Geographic variation in the aerial song of the Short-billed Dowitcher (Aves, Scolopacidae)

The complex aerial song of the Short-billed Dowitcher (Limnodromus griseus) is described, and recordings from northern British Columbia (subspecies caurinus), northern Manitoba (hendersoni), and Labrador (griseus) are analyzed. The song is a stereotyped sequence of one to five units that are repeated rapidly and increase successively in duration. Each song unit consists of three readily distinguished element types (I, II, III), which form graded series occurring in fixed sequence. Song structure and element types are similar in all subspecies, but significant quantitative differences exist; the central subspecies (hendersoni) is clearly distinguished from the other two, in particular. These geographic differences are slight in comparison with primary song in many species of Oscines.

The distributive lattice free product as a sublattice of the abelian l-group free product

This paper establishes an important link between the class of abelian l-groups and the class of distributive lattices with a distinguished element. This is accomplished by describing the distributive lattice free product of a family of abelian l-groups as a naturally generated sublattice of their abelian l-group free product.

Localizations of Linked Quaternionic Mappings

Let G and B be abelian groups with G having exponent 2 and a distinguished element –1. In [7] we defined a linked quaternionic mapping to be a map q : G × G → B satisfying the following properties:(A) q is symmetric and bilinear(B) q(a, a) = q(a, – 1) for every a ∈ G, and(L) q(a, b) = q(c, d) implies there exists x ∈ G such that q(a, b) = q(a, x) and q(c, d) = q(c, x).A form (of dimension n over q) is a symbol φ = 〈a1, …, an〉 with a1, …, an ∈ G. The determinant and Hasse invariant of such a form φ are

On a problem of MacDowell and Specker

Let T extend the theory P of Peano arithmetic, and suppose . Form from a model , in analogy to the way in which the ordered ring of integers is formed from the standard model of arithmetic. Let P′ and T′ be the corresponding analogues of P and T respectively. Now consider the group . In [5] MacDowell and Specker set out to determine the structure of such groups. (The precise statement in [5] refers to the ring of integers rather than the ordered ring. However, as pointed out to us by J. Knight, since Lagrange's Theorem that a positive integer is the sum of four squares is provable in the analogue of P′ for rings (see, for example, the proof in [7, p. 102]), the set of positive elements is definable in the ring, and consequently, so is the ordering. Thus, for the present purpose it makes no difference which of the two structures is used. Of course, one needs the ordering to discuss end extensions, as considered in [5]. On the other hand, one should be aware that in Pr′ one cannot define an ordering, where the theory Pr′ is the theory of the group of integers with distinguished element 1, 〈Z, +, 1〉. The constant 1 is needed so that divisibility mod n can be expressed. We will return to this point later.) In §1 we shall outline the results in this direction obtained in [5].Lipshitz and Nadel, unaware that a similar question had been posed and investigated in [5] (though, of course aware that [5] contained the celebrated results on end extensions) set out to characterize those models 〈A, +〉 of Pr = Presburger Arithmetic (the complete theory of 〈ω, +〉) which can be expanded to models 〈A, +, ·, 0, 1, ≤〉 of P. They were able to give a complete characterization for countable models 〈A, +〉 in [4], which we describe in §2.