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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