On Some Applications of Games for Härtig Quantifier

✍ Scribed by Michal Krynicki

• Publisher: John Wiley and Sons
• Year: 1987
• Tongue: English
• Weight: 655 KB
• Volume: 33
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19870330411

✦ Synopsis

71, ) ) E T, iff (Vi, j 5 n) (ai < a j o bi < b j ) .

It is easy to see that each equivalence class of r" (rb) is either a nontrivial segment of the given ordering which has a power equal to Card ( A ) (Card ( B ) ) or it is a one element subset. Moreover, if (a"a, bnb) E r t r then we have Card (a/.") = Card ( A ) iff Card (b/rb) = Card ( B ) .

By this observation we infer that the condition 2(e) in Definition 1.1 is satisfied. The verification of the other conditions is simple. Now let (x be an ordinal. We define the relation R on w, x o, by

Let X be the restriction of R to w, x o. We put 9l = (w, x w,, R) and ' 23 = (w, x w , S).