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53
Formal Definition of a Conceptual Language for the Description and Manipulation of Information Models
 Information Systems
, 1993
"... Conceptual data modelling techniques aim at the representation of data at a high level of abstraction. ..."
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Cited by 85 (45 self)
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Conceptual data modelling techniques aim at the representation of data at a high level of abstraction.
On the Foundations of Final Semantics: NonStandard Sets, Metric Spaces, Partial Orders
 PROCEEDINGS OF THE REX WORKSHOP ON SEMANTICS: FOUNDATIONS AND APPLICATIONS, VOLUME 666 OF LECTURE NOTES IN COMPUTER SCIENCE
, 1998
"... Canonical solutions of domain equations are shown to be final coalgebras, not only in a category of nonstandard sets (as already known), but also in categories of metric spaces and partial orders. Coalgebras are simple categorical structures generalizing the notion of postfixed point. They are ..."
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Cited by 48 (10 self)
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Canonical solutions of domain equations are shown to be final coalgebras, not only in a category of nonstandard sets (as already known), but also in categories of metric spaces and partial orders. Coalgebras are simple categorical structures generalizing the notion of postfixed point. They are also used here for giving a new comprehensive presentation of the (still) nonstandard theory of nonwellfounded sets (as nonstandard sets are usually called). This paper is meant to provide a basis to a more general project aiming at a full exploitation of the finality of the domains in the semantics of programming languages  concurrent ones among them. Such a final semantics enjoys uniformity and generality. For instance, semantic observational equivalences like bisimulation can be derived as instances of a single `coalgebraic' definition (introduced elsewhere), which is parametric of the functor appearing in the domain equation. Some properties of this general form of equivalence are also studied in this paper.
A Notation for Lambda Terms I: A Generalization of Environments
 THEORETICAL COMPUTER SCIENCE
, 1994
"... A notation for lambda terms is described that is useful in contexts where the intensions of these terms need to be manipulated. This notation uses the scheme of de Bruijn for eliminating variable names, thus obviating ffconversion in comparing terms. This notation also provides for a class of terms ..."
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Cited by 33 (12 self)
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A notation for lambda terms is described that is useful in contexts where the intensions of these terms need to be manipulated. This notation uses the scheme of de Bruijn for eliminating variable names, thus obviating ffconversion in comparing terms. This notation also provides for a class of terms that can encode other terms together with substitutions to be performed on them. The notion of an environment is used to realize this `delaying' of substitutions. The precise mechanism employed here is, however, more complex than the usual environment mechanism because it has to support the ability to examine subterms embedded under abstractions. The representation presented permits a ficontraction to be realized via an atomic step that generates a substitution and associated steps that percolate this substitution over the structure of a term. The operations on terms that are described also include ones for combining substitutions so that they might be performed simultaneously. Our notatio...
A FixedPoint Approach to Stable Matchings and Some Applications
, 2001
"... We describe a fixedpoint based approach to the theory of bipartite stable matchings. By this, we provide a common framework that links together seemingly distant results, like the stable marriage theorem of Gale and Shapley [11], the MenelsohnDulmage theorem [21], the KunduLawler theorem [19], Ta ..."
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Cited by 30 (5 self)
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We describe a fixedpoint based approach to the theory of bipartite stable matchings. By this, we provide a common framework that links together seemingly distant results, like the stable marriage theorem of Gale and Shapley [11], the MenelsohnDulmage theorem [21], the KunduLawler theorem [19], Tarski's fixed point theorem [32], the CantorBernstein theorem, Pym's linking theorem [22, 23] or the monochromatic path theorem of Sands et al. [29]. In this framework, we formulate a matroidgeneralization of the stable marriage theorem and study the lattice structure of generalized stable matchings. Based on the theory of lattice polyhedra and blocking polyhedra, we extend results of Vande Vate [33] and Rothblum [28] on the bipartite stable matching polytope.
On the Foundations of Final Coalgebra Semantics: nonwellfounded sets, partial orders, metric spaces
, 1998
"... ..."
Nonexistence of Universal Orders in Many Cardinals
 Journal of Symbolic Logic
, 1992
"... Our theme is that not every interesting question in set theory is independent of ZF C. We give an example of a first order theory T with countable D(T) which cannot have a universal model at ℵ1 without CH; we prove in ZF C a covering theorem from the hypothesis of the existence of a universal model ..."
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Cited by 19 (15 self)
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Our theme is that not every interesting question in set theory is independent of ZF C. We give an example of a first order theory T with countable D(T) which cannot have a universal model at ℵ1 without CH; we prove in ZF C a covering theorem from the hypothesis of the existence of a universal model for some theory; and we prove — again in ZFC — that for a large class of cardinals there is no universal linear order (e.g. in every ℵ1 < λ < 2 ℵ0). In fact, what we show is that if there is a universal linear order at a regular λ and its existence is not a result of a trivial cardinal arithmetical reason, then λ “resembles ” ℵ1 — a cardinal for which the consistency of having a universal order is known. As for singular cardinals, we show that for many singular cardinals, if they are not strong limits then they have no universal linear order. As a result of the non existence of a universal linear order, we show the nonexistence of universal models for all theories possessing the strict order property (for example, ordered fields and groups, Boolean algebras, padic rings and fields, partial orders, models of PA and so on).
Subgroups of small index in infinite symmetric groups
 Bull. London Math. Soc
, 1986
"... Throughout this paper Q will denote an infinite set, S: = Sym(Q) and G is a subgroup of S. If n: = Q, the cardinal of Q, then .S  = 2". Working in ZFC, set theory with Axiom of Choice (AC), we shall be seeking the subgroups G with \S: G \ < 2". If A £ Q then S ^ (respectively G{A}) d ..."
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Cited by 17 (0 self)
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Throughout this paper Q will denote an infinite set, S: = Sym(Q) and G is a subgroup of S. If n: = Q, the cardinal of Q, then .S  = 2". Working in ZFC, set theory with Axiom of Choice (AC), we shall be seeking the subgroups G with \S: G \ < 2". If A £ Q then S ^ (respectively G{A}) denotes the setwise stabiliser of A in S (respectively in G); 5(A) and G(A) denote pointwise stabilisers; we identify S(A) with Sym(fi —A). A subset £ of Q such that Z  = Q —1  = O  is known as a moiety ofQ. Suppose now that Q  = n = Ko. If there is a finite subset A of Q such that 5(A) ^ G then certainly \S:G \ ^ Xo. Our theme is a rather strong converse: THEOREM 1. Ifn = K0 and \S:G \ < 2 N » then there is a finite subset Ao ofQ such that S(Ao) ^G ^ 5{Ao}. Notice that the case Ao = 0 can arise; it corresponds precisely to the possibility that G = S. We emphasize that our proof does not need the Continuum Hypothesis (CH). LEMMA. If Fl5 T2 are infinite subsets of Cl such that \Tl 0 T2 \ = \TX U T2  then
Long Finite Sequences
, 2001
"... Let k be a positive integer. There is a longest finite sequence x 1 ,...,x n in k letters in which no consecutive block x i ,...,x 2i is a subsequence of any other consecutive block x j ,...,x 2j . Let n(k) be this longest length. We prove that n(1) = 3, n(2) = 11, and n(3) is incomprehensibly large ..."
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Cited by 13 (4 self)
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Let k be a positive integer. There is a longest finite sequence x 1 ,...,x n in k letters in which no consecutive block x i ,...,x 2i is a subsequence of any other consecutive block x j ,...,x 2j . Let n(k) be this longest length. We prove that n(1) = 3, n(2) = 11, and n(3) is incomprehensibly large. We give a lower bound for n(3) in terms of the familiar Ackerman hierarchy. We also give asymptotic upper and lower bounds for n(k). We view n(3) as a particularly elemental description of an incomprehensibly large integer. Related problems involving binary sequences (two letters) are also addressed. We also report on some recent computer explorations of R. Dougherty which we use to raise the lower bound for n(3). TABLE OF CONTENTS 1. Finiteness, and n(1),n(2). 2. Sequences of fixed length sequences. 3. The Main Lemma. 4. Lower bound for n(3). 5. The function n(k). 6. Related problems and computer explorations. 1. FINITENESS, AND n(1),n(2) We use Z for the set of all integers, Z + f...
Complete positive group presentations
 Preprint; ArXiv math.GR/0111275. GROUPS OF FRACTIONS 33
"... Abstract. A combinatorial property of prositive group presentations, called completeness, is introduced, with an effective criterion for recognizing complete presentations, and an iterative method for completing an incomplete presentation. We show how to directly read several properties of the assoc ..."
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Cited by 12 (10 self)
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Abstract. A combinatorial property of prositive group presentations, called completeness, is introduced, with an effective criterion for recognizing complete presentations, and an iterative method for completing an incomplete presentation. We show how to directly read several properties of the associated monoid and group from a complete presentation: cancellativity or existence of common multiples in the case of the monoid, or isoperimetric inequality in the case of the group. In particular, we obtain a new criterion for recognizing that a monoid embeds in a group of fractions. Typical presentations eligible for the current approach are the standard presentations of the Artin groups and the Heisenberg group.
A Formal Description of Verdi
, 1990
"... This paper will be most easily appreciated by the reader with some prior knowledge of Mathematical Logic [8, 19], Set Theory [11], and Denotational Semantics [9, 18, 20]. Verdi differs from its predecessor mVerdi [4] in several significant ways: ..."
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Cited by 10 (5 self)
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This paper will be most easily appreciated by the reader with some prior knowledge of Mathematical Logic [8, 19], Set Theory [11], and Denotational Semantics [9, 18, 20]. Verdi differs from its predecessor mVerdi [4] in several significant ways: