A strong partition cardinal above Θ

A strong partition cardinal above Θ

Assuming ZF + DC , we prove that if there exists a strong partition cardinal greater than Θ , then (1) there is an inner model of ZF + AD + DC + R # exists, and (2) there is an inner model of ZF + AD + DC + ( ∃ κ > Θ ) ( κ is measurable). Here Θ is the supremum of the ordinals which are the surje...

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Veröffentlicht in:Archive for mathematical logic 2017-05, Vol.56 (3-4), p.403-421
1. Verfasser: Cunningham, Daniel W.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
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Zusammenfassung:Assuming ZF + DC , we prove that if there exists a strong partition cardinal greater than Θ , then (1) there is an inner model of ZF + AD + DC + R # exists, and (2) there is an inner model of ZF + AD + DC + ( ∃ κ > Θ ) ( κ is measurable). Here Θ is the supremum of the ordinals which are the surjective image of the set of reals R .
ISSN:0933-5846
1432-0665
DOI:10.1007/s00153-017-0529-8