Dense orderings, partitions and weak forms of choice

Carlos González

Fundamenta Mathematicae (1995)

  • Volume: 147, Issue: 1, page 11-25
  • ISSN: 0016-2736

Abstract

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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

How to cite

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González, Carlos. "Dense orderings, partitions and weak forms of choice." Fundamenta Mathematicae 147.1 (1995): 11-25. <http://eudml.org/doc/212070>.

@article{González1995,
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},
author = {González, Carlos},
journal = {Fundamenta Mathematicae},
keywords = {weak forms of choice; relative consistency; independence; dense orders; partition properties; ZF},
language = {eng},
number = {1},
pages = {11-25},
title = {Dense orderings, partitions and weak forms of choice},
url = {http://eudml.org/doc/212070},
volume = {147},
year = {1995},
}

TY - JOUR
AU - González, Carlos
TI - Dense orderings, partitions and weak forms of choice
JO - Fundamenta Mathematicae
PY - 1995
VL - 147
IS - 1
SP - 11
EP - 25
AB - 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
LA - eng
KW - weak forms of choice; relative consistency; independence; dense orders; partition properties; ZF
UR - http://eudml.org/doc/212070
ER -

References

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  1. [1] J. D. Halpern and P. E. Howard, Cardinals m such that 2m = m, Proc. Amer. Math. Soc. 26 (1970), 487-490. Zbl0223.02055
  2. [2] T. Jech, The Axiom of Choice, North-Holland, Amsterdam, 1973. Zbl0259.02051
  3. [3] A. Levy, The independence of various definitions of finiteness, Fund. Math. 46 (1958), 1-13. Zbl0089.00702
  4. [4] D. Pincus, Zermelo-Fraenkel consistency results by Fraenkel-Mostowski methods, J. Symbolic Logic 37 (1972), 721-743. Zbl0268.02043
  5. [5] J. G. Rosenstein, Linear Orderings, Academic Press, New York, 1982. 
  6. [6] G. Sageev, An independence result concerning the axiom of choice, Ann. Math. Logic 8 (1975), 1-184. Zbl0306.02060
  7. [7] A. Tarski, Sur les ensembles finis, Fund. Math. 6 (1924), 45-95. Zbl50.0135.02

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