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A notion of rank in set theory without choice

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Abstract.

 Starting from the definition of `amorphous set' in set theory without the axiom of choice, we propose a notion of rank (which will only make sense for, at most, the class of Dedekind finite sets), which is intended to be an analogue in this situation of Morley rank in model theory.

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Authors and Affiliations

  1. University of Leeds, School of Mathematics, Leeds LS2 9JT, U.K. e-mail: pmtjkt@amsta.leeds.ac.uk, , , , , , GB

    G.S. Mendick & J.K. Truss

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  1. G.S. Mendick
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  2. J.K. Truss
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Additional information

Received: 22 September 2000 / Revised version: 14 May 2002 Published online: 19 December 2002

The research of the first author was supported by the SERC.

Mathematics Subject Classification (2000): 03E25

Key words or phrases: Rank – Degree – Amorphous

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Mendick, G., Truss, J. A notion of rank in set theory without choice. Arch. Math. Logic 42, 165–178 (2003). https://doi.org/10.1007/s00153-002-0164-9

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  • DOI: https://doi.org/10.1007/s00153-002-0164-9

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