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HSP type theorems in the category of posets

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Mathematical Foundations of Programming Semantics (MFPS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 598))

Abstract

This paper introduces the notion of a theory based on posets and HSP or Birkhoff subcategories thereof. It turns out that the nature of these subcategories depends on what is meant by subobject. The correspondence between subcategories does not hold as it does in sets, primarily because the axiom of choice (in the form that epimorphisms split) totally fails in posets. Although equations, suitably generalized to include inequalities, determine HSP subcategories, the converse fails and it may be necessary to iterate the process of forming the subcategories by means of equations and inequalities.

This research has been supported by grants from the NSERC of Canada and the FCAR du Québec

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Authors
  1. Michael Barr
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Editor information

Stephen Brookes Michael Main Austin Melton Michael Mislove David Schmidt

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© 1992 Springer-Verlag Berlin Heidelberg

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Barr, M. (1992). HSP type theorems in the category of posets. In: Brookes, S., Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Semantics. MFPS 1991. Lecture Notes in Computer Science, vol 598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55511-0_11

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  • DOI: https://doi.org/10.1007/3-540-55511-0_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55511-7

  • Online ISBN: 978-3-540-47194-3

  • eBook Packages: Springer Book Archive

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