On the Existence of Atomic Models

Laskowski, M. C.; Shelah, S.

J. Symbolic Logic, Tome 58 (1993) no. 1, p. 1189-1194 / Harvested from Project Euclid

Résumé

We give an example of a countable theory $T$ such that for every cardinal $\lambda \geq \aleph_2$ there is a fully indiscernible set $A$ of power $\lambda$ such that the principal types are dense over $A$, yet there is no atomic model of $T$ over $A$. In particular, $T(A)$ is a theory of size $\lambda$ where the principal types are dense, yet $T(A)$ has no atomic model.

Publié le : 1993-12-14
Classification:

@article{1183744369,
     author = {Laskowski, M. C. and Shelah, S.},
     title = {On the Existence of Atomic Models},
     journal = {J. Symbolic Logic},
     volume = {58},
     number = {1},
     year = {1993},
     pages = { 1189-1194},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183744369}
}

Laskowski, M. C.; Shelah, S. On the Existence of Atomic Models. J. Symbolic Logic, Tome 58 (1993) no. 1, pp.  1189-1194. http://gdmltest.u-ga.fr/item/1183744369/