Weak Covering at Large Cardinals

✍ Scribed by Ralf - Dieter Schindler

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 408 KB
• Volume: 43
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19970430103

✦ Synopsis

Abstract

We show that weakly compact cardinals are the smallest large cardinals k where k^+^ < k^+^ is impossible provided 0^#^ does not exist. We also show that if k^+^^Kc^ < k^+^ for some k being weakly compact (where K^c^ is the countably complete core model below one strong cardinal), then there is a transitive set M with M ⊨ ZFC + “there is a strong cardinal”.