The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice

✍ Scribed by Paul Howard; Jean E. Rubin

• Book ID: 102941943
• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 541 KB
• Volume: 42
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19960420133

✦ Synopsis

Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 ' 0 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second.