Elementary Extensions of Countable Models of Set Theory

Hutchinson, John E.

J. Symbolic Logic, Tome 41 (1976) no. 1, p. 139-145 / Harvested from Project Euclid

Résumé

We prove the following extension of a result of Keisler and Morley. Suppose $\mathscr{U}$ is a countable model of ZFC and $c$ is an uncountable regular cardinal in $\mathscr{U}$. Then there exists an elementary extension of $\mathscr{U}$ which fixes all ordinals below $c$, enlarges $c$, and either (i) contains or (ii) does not contain a least new ordinal. Related results are discussed.

Publié le : 1976-03-14
Classification:

@article{1183739723,
     author = {Hutchinson, John E.},
     title = {Elementary Extensions of Countable Models of Set Theory},
     journal = {J. Symbolic Logic},
     volume = {41},
     number = {1},
     year = {1976},
     pages = { 139-145},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183739723}
}

Hutchinson, John E. Elementary Extensions of Countable Models of Set Theory. J. Symbolic Logic, Tome 41 (1976) no. 1, pp.  139-145. http://gdmltest.u-ga.fr/item/1183739723/