UNDEFINABILITY OF KAPPA-WELL-ORDERINGS IN L-INFINITY-KAPPA

Authors
OIKKONEN J
Citation
J. Oikkonen, UNDEFINABILITY OF KAPPA-WELL-ORDERINGS IN L-INFINITY-KAPPA, The Journal of symbolic logic, 62(3), 1997, pp. 999-1020
Citations number
22
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
The Journal of symbolic logic → ACNP
ISSN journal
00224812
Volume
62
Issue
3
Year of publication
1997
Pages
999 - 1020
Database
ISI
SICI code
0022-4812(1997)62:3<999:UOKIL>2.0.ZU;2-3
Abstract
We prove that the class of trees with no branches of cardinality great er than or equal to kappa is not RPC definable in L-infinity kappa whe n kappa is regular. Earlier such a result was known for Lkappa+kappa u nder the assumption kappa(<kappa) = kappa. Our main result is actually proved in a stronger form which covers also L-infinity lambda (and ma kes sense there) for every strong limit cardinal lambda > kappa of cof inality kappa.