# Borel and Baire reducibility

Fundamenta Mathematicae (2000)

- Volume: 164, Issue: 1, page 61-69
- ISSN: 0016-2736

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topFriedman, Harvey. "Borel and Baire reducibility." Fundamenta Mathematicae 164.1 (2000): 61-69. <http://eudml.org/doc/212448>.

@article{Friedman2000,

abstract = {We prove that a Borel equivalence relation is classifiable by countable structures if and only if it is Borel reducible to a countable level of the hereditarily countable sets. We also prove the following result which was originally claimed in [FS89]: the zero density ideal of sets of natural numbers is not classifiable by countable structures.},

author = {Friedman, Harvey},

journal = {Fundamenta Mathematicae},

keywords = {Borel equivalence relation; analytic equivalence relation; Borel reduction; Baire reduction},

language = {eng},

number = {1},

pages = {61-69},

title = {Borel and Baire reducibility},

url = {http://eudml.org/doc/212448},

volume = {164},

year = {2000},

}

TY - JOUR

AU - Friedman, Harvey

TI - Borel and Baire reducibility

JO - Fundamenta Mathematicae

PY - 2000

VL - 164

IS - 1

SP - 61

EP - 69

AB - We prove that a Borel equivalence relation is classifiable by countable structures if and only if it is Borel reducible to a countable level of the hereditarily countable sets. We also prove the following result which was originally claimed in [FS89]: the zero density ideal of sets of natural numbers is not classifiable by countable structures.

LA - eng

KW - Borel equivalence relation; analytic equivalence relation; Borel reduction; Baire reduction

UR - http://eudml.org/doc/212448

ER -

## References

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- [Ke94] A. S. Kechris, Classical Descriptive Set Theory, Grad. Texts in Math. 156, Springer, 1994.
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