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ArticleOriginal scientific text

Title

Dense orderings, partitions and weak forms of choice

Authors 1

Affiliations

  1. Centro de Lógica, Epistemologia e História da Ciência, Universidade Estadual de Campinas (Unicamp), P.O. Box 6133, 13081-000 Campinas SP, Brazil

Abstract

We investigate the relative consistency and independence of statements which imply the existence of various kinds of dense orders, including dense linear orders. We study as well the relationship between these statements and others involving partition properties. Since we work in ZF (i.e. without the Axiom of Choice), we also analyze the role that some weaker forms of AC play in this context

Bibliography

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  2. T. Jech, The Axiom of Choice, North-Holland, Amsterdam, 1973.
  3. A. Levy, The independence of various definitions of finiteness, Fund. Math. 46 (1958), 1-13.
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  5. J. G. Rosenstein, Linear Orderings, Academic Press, New York, 1982.
  6. G. Sageev, An independence result concerning the axiom of choice, Ann. Math. Logic 8 (1975), 1-184.
  7. A. Tarski, Sur les ensembles finis, Fund. Math. 6 (1924), 45-95.

Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm147/fm14712.pdf

Fundamenta Mathematicae
1995/147/1
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Pages:
11-25
Main language of publication
English
Received
1993-08-24
Accepted
1994-10-05
Published
1995
Exact and natural sciences