The Vaught Conjecture: Do Uncountable Models Count?
Baldwin, John T.
Notre Dame J. Formal Logic, Tome 48 (2007) no. 1, p. 79-92 / Harvested from Project Euclid
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We give a model theoretic proof, replacing admissible set theory by the Lopez-Escobar theorem, of Makkai's theorem: Every counterexample to Vaught's Conjecture has an uncountable model which realizes only countably many ℒ$_{ω₁,ω}$-types. The following result is new. Theorem: If a first-order theory is a counterexample to the Vaught Conjecture then it has 2\sp ℵ₁ models of cardinality ℵ₁.
Publié le : 2007-01-14
Classification:  Vaught's conjecture,  infinitary languages,  03C15,  03C45 
@article{1172787546,
     author = {Baldwin, John T.},
     title = {The Vaught Conjecture: Do Uncountable Models Count?},
     journal = {Notre Dame J. Formal Logic},
     volume = {48},
     number = {1},
     year = {2007},
     pages = { 79-92},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1172787546}
}

Baldwin, John T. The Vaught Conjecture: Do Uncountable Models Count?. Notre Dame J. Formal Logic, Tome 48 (2007) no. 1, pp.  79-92. http://gdmltest.u-ga.fr/item/1172787546/