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244
The generic filter property in nonstandard analysis
 Annals of Pure and Applied Logic
"... In this paper two new combinatorial principles in nonstandard analysis are isolated and applications are given. The second principle provides an equivalent formulation of Henson’s isomorphism property. Introduction. In his 1974 paper [He], C. Ward Henson introduced the isomorphism property (IP) for ..."
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Cited by 3 (0 self)
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In this paper two new combinatorial principles in nonstandard analysis are isolated and applications are given. The second principle provides an equivalent formulation of Henson’s isomorphism property. Introduction. In his 1974 paper [He], C. Ward Henson introduced the isomorphism property (IP
Tabu Search  Part I
, 1989
"... This paper presents the fundamental principles underlying tabu search as a strategy for combinatorial optimization problems. Tabu search has achieved impressive practical successes in applications ranging from scheduling and computer channel balancing to cluster analysis and space planning, and more ..."
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Cited by 680 (11 self)
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This paper presents the fundamental principles underlying tabu search as a strategy for combinatorial optimization problems. Tabu search has achieved impressive practical successes in applications ranging from scheduling and computer channel balancing to cluster analysis and space planning
Property and the Special Model Axiom in nonstandard analysis.
"... Abstract. We study combinatorial principles related to the Isomorphism ..."
Unifying Constructive and Nonstandard Analysis
 Bull. Symbolic Logic
, 1999
"... This paper is partly a survey of this development. In Section 2 we review the construction of the nonstandard universe N . Section 3 discusses the internal sets and functions of N . Here we present two new results for N : the @ 1 saturation principle and a characterisation of internal functions bet ..."
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Cited by 26 (5 self)
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This paper is partly a survey of this development. In Section 2 we review the construction of the nonstandard universe N . Section 3 discusses the internal sets and functions of N . Here we present two new results for N : the @ 1 saturation principle and a characterisation of internal functions
Mellin Transforms And Asymptotics: Harmonic Sums
 THEORETICAL COMPUTER SCIENCE
, 1995
"... This survey presents a unified and essentially selfcontained approach to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics, discrete probabilistic models, and the averagecase analysis of algorithms. It relies on the Mellin transform, a close relative of the i ..."
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Cited by 202 (12 self)
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This survey presents a unified and essentially selfcontained approach to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics, discrete probabilistic models, and the averagecase analysis of algorithms. It relies on the Mellin transform, a close relative
The strength of nonstandard analysis
 J. Symb. Logic
, 1986
"... A weak theory nonstandard analysis, with types at all finite levels over both the integers and hyperintegers, is developed as a possible framework for reverse mathematics. In this weak theory, we investigate the strength of standard part principles and saturation principles which are often used in p ..."
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Cited by 15 (2 self)
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A weak theory nonstandard analysis, with types at all finite levels over both the integers and hyperintegers, is developed as a possible framework for reverse mathematics. In this weak theory, we investigate the strength of standard part principles and saturation principles which are often used
Constructivism and Proof Theory
, 2003
"... Introduction to the constructive point of view in the foundations of mathematics, in
particular intuitionism due to L.E.J. Brouwer, constructive recursive mathematics
due to A.A. Markov, and Bishop’s constructive mathematics. The constructive interpretation
and formalization of logic is described. F ..."
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Cited by 205 (4 self)
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principles which are valid for choice sequences are discussed.
The second half of the article deals with some aspects of proof theory, i.e.,
the study of formal proofs as combinatorial objects. Gentzen’s fundamental contributions
are outlined: his introduction of the socalled Gentzen systems which use
Transfer Principle Proof Tactic for Nonstandard Analysis
, 2005
"... This paper describes a type constructor for nonstandard extensions of arbitrary types, generalizing the previous formalization of nonstandard analysis in Isabelle by Fleuriot and Paulson [1]. In addition to numeric types, nonstandard extensions of function spaces and set types also prove useful—they ..."
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—they provide an elegant way to define internal functions and internal sets. The paper also describes an implementation of the transfer principle of nonstandard analysis as an Isabelle proof tactic. When applied to an appropriate subgoal, the transfer tactic replaces the subgoal with a logically equivalent one
A constructive approach to nonstandard analysis
, 1994
"... In the present paper we introduce a constructive theory of nonstandard arithmetic in higher types. The theory is intended as a framework for developing elementary nonstandard analysis constructively. More specifically, the theory introduced is a conservative extension of HA ” + AC. A predicate for d ..."
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Cited by 13 (4 self)
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In the present paper we introduce a constructive theory of nonstandard arithmetic in higher types. The theory is intended as a framework for developing elementary nonstandard analysis constructively. More specifically, the theory introduced is a conservative extension of HA ” + AC. A predicate
Intrinsic Properties and Combinatorial Principles
"... Three objections have recently been levelled at the analysis of intrinsicness offered by Rae Langton and David Lewis. While these objections do seem telling against the particular theory Langton and Lewis offer, they do not threaten the broader strategy Langton and Lewis adopt: defining intrinsicnes ..."
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Cited by 2 (0 self)
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intrinsicness in terms of combinatorial features of properties. I show how to amend their theory to overcome the objections without abandoning the strategy. Three objections have recently been levelled at the analysis of intrinsicness in Rae Langton and David Lewis’s “Defining ‘Intrinsic”’. Yablo (1993) has
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244