Reflection implies the SCH
Fundamenta Mathematicae (2008)
- Volume: 198, Issue: 2, page 95-111
- ISSN: 0016-2736
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topSaharon Shelah. "Reflection implies the SCH." Fundamenta Mathematicae 198.2 (2008): 95-111. <http://eudml.org/doc/286118>.
@article{SaharonShelah2008,
abstract = {We prove that, e.g., if μ > cf(μ) = ℵ₀ and $μ > 2^\{ℵ₀\}$ and every stationary family of countable subsets of μ⁺ reflects in some subset of μ⁺ of cardinality ℵ₁, then the SCH for μ⁺ holds (moreover, for μ⁺, any scale for μ⁺ has a bad stationary set of cofinality ℵ₁). This answers a question of Foreman and Todorčević who get such a conclusion from the simultaneous reflection of four stationary sets.},
author = {Saharon Shelah},
journal = {Fundamenta Mathematicae},
keywords = {reflection; stationary sets; singular cardinal hypothesis; pcf},
language = {eng},
number = {2},
pages = {95-111},
title = {Reflection implies the SCH},
url = {http://eudml.org/doc/286118},
volume = {198},
year = {2008},
}
TY - JOUR
AU - Saharon Shelah
TI - Reflection implies the SCH
JO - Fundamenta Mathematicae
PY - 2008
VL - 198
IS - 2
SP - 95
EP - 111
AB - We prove that, e.g., if μ > cf(μ) = ℵ₀ and $μ > 2^{ℵ₀}$ and every stationary family of countable subsets of μ⁺ reflects in some subset of μ⁺ of cardinality ℵ₁, then the SCH for μ⁺ holds (moreover, for μ⁺, any scale for μ⁺ has a bad stationary set of cofinality ℵ₁). This answers a question of Foreman and Todorčević who get such a conclusion from the simultaneous reflection of four stationary sets.
LA - eng
KW - reflection; stationary sets; singular cardinal hypothesis; pcf
UR - http://eudml.org/doc/286118
ER -
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