The Structure of Amorphous Sets

@article{Truss1995TheSO,
  title={The Structure of Amorphous Sets},
  author={J. K. Truss},
  journal={Ann. Pure Appl. Logic},
  year={1995},
  volume={73},
  pages={191-233}
}
A set is said to be amorphous if it is infinite, but is not the disjoint union of two infinite subsets. Thus amorphous sets can exist only if the axiom of choice is false. We give a general study of the structure which an amorphous set can carry, with the object of eventually obtaining a complete classification. The principal types of amorphous set we distinguish are the following: amorphous sets not of projective type, either bounded or unbounded (depending on whether there is a bound on the… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-7 of 7 references

Small sets with large power sets

  • G. P. Monro
  • Bull. Australian Math. Sot
  • 1973

Lectures on set theory with particular emphasis on the method of forcing

  • T. Jech
  • Lecture Notes in Math. Vol. 217 (Springer, Berlin…
  • 1971

The Boolean prime ideal theorem does not imply the axiom of choice

  • J. D. Halpern, A. Levy
  • Axiomatic set theory, Proc. Symp. Pure Math., Vol…
  • 1971

Cancellation laws in the arithmetic of cardinals

  • A. Tarski
  • Fund. Math
  • 1949

Uber die Unabhlngigkeit des Auswahlaxioms und einiger seiner Folgerungen

  • A. Lindenbaum, A. Mostowski
  • C.R. des Seances de la Societt des Sciences et…
  • 1938

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