Open Access
June 2017 Real sets
George Janelidze, Ross Street
Tbilisi Math. J. 10(3): 23-49 (June 2017). DOI: 10.1515/tmj-2017-0101


After reviewing a universal characterization of the extended positive real numbers published by Denis Higgs in 1978, we define a category which provides an answer to the questions:

  • what is a set with half an element?

  • what is a set with $\pi$ elements?

The category of these extended positive real sets is equipped with a countable tensor product. We develop somewhat the theory of categories with countable tensors; we call the commutative such categories series monoidal and conclude by only briefly mentioning the non-commutative possibility called $\omega$-monoidal. We include some remarks on sets having cardinalities in $[−\infty, \infty]$.

Funding Statement

The first author gratefully acknowledges the support of the South African National Research Foundation.
The second author gratefully acknowledges the support of Australian Research Council Discovery Grants DP1094883, DP130101969 and DP160101519.


Download Citation

George Janelidze. Ross Street. "Real sets." Tbilisi Math. J. 10 (3) 23 - 49, June 2017.


Received: 15 May 2017; Revised: 7 September 2017; Published: June 2017
First available in Project Euclid: 20 April 2018

zbMATH: 06786039
MathSciNet: MR3707129
Digital Object Identifier: 10.1515/tmj-2017-0101

Primary: 18D10
Secondary: 18D20 , 20M14 , 28A20

Keywords: abstract addition , biproduct , commutative monoid , direct sum , magnitude module , series monoidal category

Rights: Copyright © 2017 Tbilisi Centre for Mathematical Sciences

Vol.10 • No. 3 • June 2017
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