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Infinite Ordered Sets, A Recursive Perspective

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Ordered Sets

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 83))

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Abstract

This work surveys the development of the theory of infinite ordered sets along the lines suggested by recursion theory. Since recursion theory is principally concerned with explicit effective constructions, this line of research retains much of the character of the mathematics of finite ordered sets. There are two distinct categories into which the results fall: the first is concerned with individual infinite ordered sets on which the ordering can be mechanically determined, while the second concerns whether the elementary sentences true in a given class of ordered sets can be distinguished by an algorithm. Roughly, an elementary sentence is one that refers to the elements of an ordered set rather than, say, sets of elements. “Width 3” is a notion expressible by an elementary sentence, but “finite width” cannot be expressed even by a set of such sentences. The requisite background in recursion theory and in the logic of elementary sentences can be found in Barwise [1977].

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Authors and Affiliations

  1. Department of Mathematics, Computer Science, and Statistics, University of South Carolina, Columbia, South Carolina, 09208, USA

    George F. McNulty

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  1. George F. McNulty
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Editors and Affiliations

  1. Department of Mathematics and Statistics, The University of Calgary, Canada

    Ivan Rival

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© 1982 D. Reidel Publishing Company

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McNulty, G.F. (1982). Infinite Ordered Sets, A Recursive Perspective. In: Rival, I. (eds) Ordered Sets. NATO Advanced Study Institutes Series, vol 83. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7798-3_9

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  • DOI: https://doi.org/10.1007/978-94-009-7798-3_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-7800-3

  • Online ISBN: 978-94-009-7798-3

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