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Infinitary Addition, Real Numbers, and Taut Monads

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A Correction to this article was published on 12 May 2018

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Abstract

We make various observations on infinitary addition in the context of the series monoids introduced in our previous paper on real sets. In particular, we explore additional conditions on such monoids suggested by Tarski’s Arithmetic of Cardinal Algebras, and present a monad-theoretic construction that generalizes our construction of paradoxical real numbers.

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Change history

  • 12 May 2018

    In the original publication of the article, Eq. (3.24) was published incorrectly. The corrected equation is given in this correction article. The original article has been corrected.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7701, South Africa

    George Janelidze

  2. Mathematics Department, Macquarie University, Sydney, NSW, 2109, Australia

    Ross Street

Authors
  1. George Janelidze
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  2. Ross Street
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Corresponding author

Correspondence to George Janelidze.

Additional information

Communicated by Maria Manuel Clementino.

Dedicated to Bob Lowen, creator of APCS.

George Janelidze gratefully acknowledges the support of the South African National Research Foundation. Ross Street gratefully acknowledges the support of Australian Research Council Discovery Grants DP1094883, DP130101969 and DP160101519.

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Janelidze, G., Street, R. Infinitary Addition, Real Numbers, and Taut Monads. Appl Categor Struct 26, 1047–1064 (2018). https://doi.org/10.1007/s10485-018-9524-4

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  • DOI: https://doi.org/10.1007/s10485-018-9524-4

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