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Undefinability of κ-well-orderings in L∞κ

Published online by Cambridge University Press:  12 March 2014

Juha Oikkonen
Juha Oikkonen*
Affiliation:
Helsingin Yliopisto, Matematiikan Laiton, PI 4 (Yliopistonkatu 5), 00014 Helsingin Yliopisto, Finland, E-mail: oikkonen@cc.helsinki.fi
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Abstract

We prove that the class of trees with no branches of cardinality ≤ κ is not RPC definable in L∞κ when κ is regular. Earlier such a result was known for under the assumption κ<κ = κ. Our main result is actually proved in a stronger form which covers also L∞κ (and makes sense there) for every strong limit cardinal λ < κ of cofinality κ.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 3 , September 1997 , pp. 999 - 1020
Copyright
Copyright © Association for Symbolic Logic 1997

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