TY - JOUR
T1 - The universality spectrum of stable unsuperstable theories
AU - Kojman, Menachem
AU - Shelah, Saharon
PY - 1992/7/3
Y1 - 1992/7/3
N2 - Kojman, M. and S. Shelah, The universality spectrum of stable unsuperstable theories, Annals of Pure and Applied Logic 58 (1992) 57-72. It is shown that if T is stable unsuperstable, and א1<λ = cf λ<2א0, or 2א0<μ+<λ = cf λ<μא0 then T has no universal model in cardinality λ, and if e.g. אω<2א0 then T has no universal model in אω. These results are generalized to κ = cf κ<κ(T) in place of א0. Also: if there is a universal model in λ>[brvbar]T[brvbar], T stable and κ<κ(T) then there is a universal tree of height κ + 1 in cardinality λ.
AB - Kojman, M. and S. Shelah, The universality spectrum of stable unsuperstable theories, Annals of Pure and Applied Logic 58 (1992) 57-72. It is shown that if T is stable unsuperstable, and א1<λ = cf λ<2א0, or 2א0<μ+<λ = cf λ<μא0 then T has no universal model in cardinality λ, and if e.g. אω<2א0 then T has no universal model in אω. These results are generalized to κ = cf κ<κ(T) in place of א0. Also: if there is a universal model in λ>[brvbar]T[brvbar], T stable and κ<κ(T) then there is a universal tree of height κ + 1 in cardinality λ.
UR - http://www.scopus.com/inward/record.url?scp=38249012980&partnerID=8YFLogxK
U2 - 10.1016/0168-0072(92)90034-W
DO - 10.1016/0168-0072(92)90034-W
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AN - SCOPUS:38249012980
SN - 0168-0072
VL - 58
SP - 57
EP - 72
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 1
ER -