# Borel completeness of some ℵ₀-stable theories

Michael C. Laskowski; Saharon Shelah

Fundamenta Mathematicae (2015)

- Volume: 229, Issue: 1, page 1-46
- ISSN: 0016-2736

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topMichael C. Laskowski, and Saharon Shelah. "Borel completeness of some ℵ₀-stable theories." Fundamenta Mathematicae 229.1 (2015): 1-46. <http://eudml.org/doc/283327>.

@article{MichaelC2015,

abstract = {We study ℵ₀-stable theories, and prove that if T either has eni-DOP or is eni-deep, then its class of countable models is Borel complete. We introduce the notion of λ-Borel completeness and prove that such theories are λ-Borel complete. Using this, we conclude that an ℵ₀-stable theory satisfies $I_\{∞,ℵ₀\}(T,λ) = 2^\{λ\}$ for all cardinals λ if and only if T either has eni-DOP or is eni-deep.},

author = {Michael C. Laskowski, Saharon Shelah},

journal = {Fundamenta Mathematicae},

keywords = {Borel complete; Borel reducibility; $\aleph _0$-stable},

language = {eng},

number = {1},

pages = {1-46},

title = {Borel completeness of some ℵ₀-stable theories},

url = {http://eudml.org/doc/283327},

volume = {229},

year = {2015},

}

TY - JOUR

AU - Michael C. Laskowski

AU - Saharon Shelah

TI - Borel completeness of some ℵ₀-stable theories

JO - Fundamenta Mathematicae

PY - 2015

VL - 229

IS - 1

SP - 1

EP - 46

AB - We study ℵ₀-stable theories, and prove that if T either has eni-DOP or is eni-deep, then its class of countable models is Borel complete. We introduce the notion of λ-Borel completeness and prove that such theories are λ-Borel complete. Using this, we conclude that an ℵ₀-stable theory satisfies $I_{∞,ℵ₀}(T,λ) = 2^{λ}$ for all cardinals λ if and only if T either has eni-DOP or is eni-deep.

LA - eng

KW - Borel complete; Borel reducibility; $\aleph _0$-stable

UR - http://eudml.org/doc/283327

ER -

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