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87
Definable sets in ordered structures
 Bull. Amer. Math. Soc. (N.S
, 1984
"... Abstract. This paper introduces and begins the study of a wellbehaved class of linearly ordered structures, the ^minimal structures. The definition of this class and the corresponding class of theories, the strongly ©minimal theories, is made in analogy with the notions from stability theory of m ..."
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Cited by 127 (8 self)
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Abstract. This paper introduces and begins the study of a wellbehaved class of linearly ordered structures, the ^minimal structures. The definition of this class and the corresponding class of theories, the strongly ©minimal theories, is made in analogy with the notions from stability theory of minimal structures and strongly minimal theories. Theorems 2.1 and 2.3, respectively, provide characterizations of Cminimal ordered groups and rings. Several other simple results are collected in §3. The primary tool in the analysis of ¿¡minimal structures is a strong analogue of "forking symmetry, " given by Theorem 4.2. This result states that any (parametrically) definable unary function in an (5minimal structure is piecewise either constant or an orderpreserving or reversing bijection of intervals. The results that follow include the existence and uniqueness of prime models over sets (Theorem 5.1) and a characterization of all N0categorical ¿¡¡minimal structures (Theorem 6.1). 1. Introduction. The
On Logics with Two Variables
 Theoretical Computer Science
, 1999
"... This paper is a survey and systematic presentation of decidability and complexity issues for modal and nonmodal twovariable logics. A classical result due to Mortimer says that the twovariable fragment of firstorder logic, denoted FO 2 , has the finite model property and is therefore decidable ..."
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Cited by 46 (9 self)
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This paper is a survey and systematic presentation of decidability and complexity issues for modal and nonmodal twovariable logics. A classical result due to Mortimer says that the twovariable fragment of firstorder logic, denoted FO 2 , has the finite model property and is therefore decidable for satisfiability. One of the reasons for the significance of this result is that many propositional modal logics can be embedded into FO 2 . Logics that are of interest for knowledge representation, for the specification and verification of concurrent systems and for other areas of computer science are often defined (or can be viewed) as extensions of modal logics by features like counting constructs, path quantifiers, transitive closure operators, least and greatest fixed points etc. Examples of such logics are computation tree logic CTL, the modal ¯calculus L¯ , or popular description logics used in artificial intelligence. Although the additional features are usually not firstorder...
Swimming of a waving plate
 Journal of Fluid Mechanics
, 1961
"... The purpose of ' this paper is to study the basic principle of fish propulsion. As a simplified model, the twodimensional potential flow over a waving plate of finite chord is treated. The solid plate, assumed to be flexible and thin, is capable of performing the motion which consists of a pro ..."
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Cited by 37 (0 self)
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The purpose of ' this paper is to study the basic principle of fish propulsion. As a simplified model, the twodimensional potential flow over a waving plate of finite chord is treated. The solid plate, assumed to be flexible and thin, is capable of performing the motion which consists of a progressing wave of given wavelength and phase velocity along the chord, the envelope of the wave train being an arbitrary function of the distance from the leading edge. The problem is solved by applying the general theory for oscillating deformable airfoils. The thrust, power required, and the energy imparted to the wake are calculated, and the propulsive efficiency is also evaluated. As a numerical example, the waving motion with linearly varying amplitude is carried out in detail. Finally, the basic mechanism of swimming is elucidated by applying the principle of action and reaction. 1.
Exploring Positive Monad Bundles And A New Heterotic Standard Model
 JHEP
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Walrasian Equilibrium without Survival: Equilibrium, Efficiency, and Remedial Policy
 welfare and development: A Festschrift in honour of Amartya K. Sen
, 1995
"... Standard general equilibrium theory excludes starvation by assuming that everybody can survive without trade. Because trade cannot harm consumers, they can therefore also survive with trade. Here this assumption is abandoned, and equilibria in which not everybody survives are investigated. A simple ..."
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Cited by 23 (15 self)
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Standard general equilibrium theory excludes starvation by assuming that everybody can survive without trade. Because trade cannot harm consumers, they can therefore also survive with trade. Here this assumption is abandoned, and equilibria in which not everybody survives are investigated. A simple example is discussed, along with possible policies which might reduce starvation. Thereafter, for economies with a continuum of agents, the usual results are established — existence of equilibrium, the two fundamental efficiency theorems of welfare economics, and core equivalence. Their validity depends on some special but not very stringent assumptions needed to deal with natural nonconvexities in each consumer’s feasible set.
Places of Algebraic Function Fields in Arbitrary Characteristic
, 2003
"... We consider the Zariski space of all places of an algebraic function field F of arbitrary characteristic and investigate its structure by means of its patch topology. We show that certain sets of places with nice properties (e.g., prime divisors, places of maximal rank, zerodimensional discret ..."
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Cited by 22 (8 self)
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We consider the Zariski space of all places of an algebraic function field F of arbitrary characteristic and investigate its structure by means of its patch topology. We show that certain sets of places with nice properties (e.g., prime divisors, places of maximal rank, zerodimensional discrete places) lie dense in this topology. Further, we give several equivalent characterizations of fields that are large, in the sense of F. Pop's Annals paper Embedding problems over large fields. We also study the question whether a field K is existentially closed in an extension field L if L admits a Krational place. In the appendix, we prove the fact that the Zariski space with the Zariski topology is quasicompact and that it is a spectral space.
Integration in valued fields
 in Algebraic Geometry and Number Theory, Progr. Math. 253, Birkhäuser
, 2006
"... Abstract. We develop a theory of integration over valued fields of residue characteristic zero. In particular we obtain new and basefield independent foundations for integration over local fields of large residue characteristic, extending results of Denef,Loeser, Cluckers. The method depends on an ..."
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Cited by 20 (2 self)
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Abstract. We develop a theory of integration over valued fields of residue characteristic zero. In particular we obtain new and basefield independent foundations for integration over local fields of large residue characteristic, extending results of Denef,Loeser, Cluckers. The method depends on an analysis of definable sets up to definable bijections. We obtain a precise description of the Grothendieck semigroup of such sets in terms of related groups over the residue field and value group. This yields new invariants of all definable bijections, as well as invariants of measure preserving bijections.