# A dichotomy theorem for mono-unary algebras

Fundamenta Mathematicae (2000)

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

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topGao, 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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- [Ga] S. Gao, The isomorphism relation between countable models and definable equivalence relations, Ph.D. dissertation, UCLA, 1998.
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- [HK] G. Hjorth and A. S. Kechris, Analytic equivalence relations and Ulm-type classifications, J. Symbolic Logic 60 (1995), 1273-1300. Zbl0847.03023
- [Ma] L. Marcus, The number of countable models of a theory of one unary function, Fund. Math. 58 (1980), 171-181. Zbl0363.02055
- [Sa] R. Sami, Polish group actions and the Vaught Conjecture, Trans. Amer. Math. Soc. 341 (1994), 335-353. Zbl0795.03069
- [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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