Affiliation:
1. Department of Mathematics & Statistics University of Helsinki Finland
2. FNWI ILLC Universiteit van Amsterdam The Netherlands
3. School of Mathematics University of Bristol UK
Abstract
AbstractWe show that the predicate “x is the power set of y” is ‐definable, if V = L[E] is an extender model constructed from a coherent sequences of extenders, provided that there is no inner model with a Woodin cardinal. Here is a predicate true of just the infinite cardinals. From this we conclude: the validities of second order logic are reducible to , the set of validities of the Härtig quantifier logic. Further we show that if no L[E] model has a cardinal strong up to one of its ℵ‐fixed points, and , the Löwenheim number of this logic, is less than the least weakly inaccessible δ, then (i) is a limit of measurable cardinals of K, and (ii) the Weak Covering Lemma holds at δ.
Funder
European Research Council
Academy of Finland