A dichotomy theorem for mono-unary algebras

Su Gao

Fundamenta Mathematicae (2000)

  • Volume: 163, Issue: 1, page 25-37
  • ISSN: 0016-2736

Abstract

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We study the isomorphism relation of invariant Borel classes of countable mono-unary algebras and prove a strong dichotomy theorem.

How to cite

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Gao, Su. "A dichotomy theorem for mono-unary algebras." Fundamenta Mathematicae 163.1 (2000): 25-37. <http://eudml.org/doc/212427>.

@article{Gao2000,
abstract = {We study the isomorphism relation of invariant Borel classes of countable mono-unary algebras and prove a strong dichotomy theorem.},
author = {Gao, Su},
journal = {Fundamenta Mathematicae},
keywords = {descriptive set theory; countable model theory; admissible set theory; Vaught conjecture; Glimm-Effros dichotomy},
language = {eng},
number = {1},
pages = {25-37},
title = {A dichotomy theorem for mono-unary algebras},
url = {http://eudml.org/doc/212427},
volume = {163},
year = {2000},
}

TY - JOUR
AU - Gao, Su
TI - A dichotomy theorem for mono-unary algebras
JO - Fundamenta Mathematicae
PY - 2000
VL - 163
IS - 1
SP - 25
EP - 37
AB - We study the isomorphism relation of invariant Borel classes of countable mono-unary algebras and prove a strong dichotomy theorem.
LA - eng
KW - descriptive set theory; countable model theory; admissible set theory; Vaught conjecture; Glimm-Effros dichotomy
UR - http://eudml.org/doc/212427
ER -

References

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  1. [Ba] J. Barwise, Admissible Sets and Structures: an Approach to Definability Theory, Perspectives in Math. Logic, Springer, Berlin, 1975. Zbl0316.02047
  2. [BK] H. Becker and A. S. Kechris, The Descriptive Set Theory of Polish Group Actions, London Math. Soc. Lecture Note Ser. 232, Cambridge Univ. Press, Cambridge, 1996. Zbl0949.54052
  3. [FS] H. Friedman and L. Stanley, A Borel reducibility theory for classes of countable structures, J. Symbolic Logic 54 (1989), 894-914. Zbl0692.03022
  4. [Ga] S. Gao, The isomorphism relation between countable models and definable equivalence relations, Ph.D. dissertation, UCLA, 1998. 
  5. [HKL] L. Harrington, A. S. Kechris and A. Louveau, A Glimm-Effros dichotomy for Borel equivalence relations, J. Amer. Math. Soc. 3 (1990), 903-928. Zbl0778.28011
  6. [HK] G. Hjorth and A. S. Kechris, Analytic equivalence relations and Ulm-type classifications, J. Symbolic Logic 60 (1995), 1273-1300. Zbl0847.03023
  7. [Ma] L. Marcus, The number of countable models of a theory of one unary function, Fund. Math. 58 (1980), 171-181. Zbl0363.02055
  8. [Sa] R. Sami, Polish group actions and the Vaught Conjecture, Trans. Amer. Math. Soc. 341 (1994), 335-353. Zbl0795.03069
  9. [St] J. R. Steel, On Vaught's Conjecture, in: Cabal Seminar 76-77, Lecture Notes in Math. 689, Springer, Berlin, 1978, 193-208. 

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