A game on partial orderings

✍ Scribed by Sakaé Fuchino; Sabine Koppelberg; Saharon Shelah

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 412 KB
• Volume: 74
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(96)00051-x

✦ Synopsis

We study the determinacy of the game G~(A) introduced in Fuchino, Koppelberg and Shelah (to appear) for uncountable regular n and several classes of partial orderings A. Among trees or Boolean algebras, we can always find an A such that G~(A) is undetermined. For the class of linear orders, the existence of such A depends on the size of ~<'~. In particular we obtain a characterization of ~<'~ = ~ in terms of determinacy of the game G~(L) for linear orders L.