A DIRECT PROOF OF A RESULT OF SHELAH

✍ Scribed by Martin Weese

• Publisher: John Wiley and Sons
• Year: 1992
• Tongue: English
• Weight: 110 KB
• Volume: 38
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19920380130

✦ Synopsis

Abstract

Shelah has shown (see [1]) that the number d, the smallest cardinality of a dominating family, is less than or equal to the number i, the smallest cardinality of a maximal independent family on ω. This was done using a downward Löwenheim‐Skolem argument. Thus it is interesting to find a direct “elementary” proof. Here we show that this can be done.