The Stability Function of a Theory
Keisler, H. Jerome
J. Symbolic Logic, Tome 43 (1978) no. 1, p. 481-486 / Harvested from Project Euclid
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Let $T$ be a complete theory with infinite models in a countable language. The stability function $g_T(\kappa)$ is defined as the supremum of the number of types over models of $T$ of power $\kappa$. It is proved that there are only six possible stability functions, namely $\kappa, \kappa + 2^\omega, \kappa^\omega, \operatorname{ded} \kappa, (\operatorname{ded} \kappa)^\omega, 2^\kappa$.
Publié le : 1978-09-14
Classification:  
@article{1183740252,
     author = {Keisler, H. Jerome},
     title = {The Stability Function of a Theory},
     journal = {J. Symbolic Logic},
     volume = {43},
     number = {1},
     year = {1978},
     pages = { 481-486},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183740252}
}

Keisler, H. Jerome. The Stability Function of a Theory. J. Symbolic Logic, Tome 43 (1978) no. 1, pp.  481-486. http://gdmltest.u-ga.fr/item/1183740252/