Undefinability of $\kappa$-Well-Orderings in $L_{\infty\kappa}$
Oikkonen, Juha
J. Symbolic Logic, Tome 62 (1997) no. 1, p. 999-1020 / Harvested from Project Euclid
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We prove that the class of trees with no branches of cardinality $\geq\kappa$ is not RPC definable in $L_{\infty\kappa}$ when $\kappa$ is regular. Earlier such a result was known for $L_{\kappa^+\kappa}$ under the assumption $\kappa^{<\kappa} = \kappa$. Our main result is actually proved in a stronger form which covers also $L_{\infty\lambda}$ (and makes sense there) for every strong limit cardinal $\lambda > \kappa$ of cofinality $\kappa$.
Publié le : 1997-09-14
Classification:  
@article{1183745309,
     author = {Oikkonen, Juha},
     title = {Undefinability of $\kappa$-Well-Orderings in $L\_{\infty\kappa}$},
     journal = {J. Symbolic Logic},
     volume = {62},
     number = {1},
     year = {1997},
     pages = { 999-1020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745309}
}

Oikkonen, Juha. Undefinability of $\kappa$-Well-Orderings in $L_{\infty\kappa}$. J. Symbolic Logic, Tome 62 (1997) no. 1, pp.  999-1020. http://gdmltest.u-ga.fr/item/1183745309/