Combinatorial Aspects of the Splitting Number

Shimon Garti, Saharon Shelah

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء

ملخص

This paper deals with the splitting number s and polarized partition relations. In the first section we define the notion of strong splitting families, and prove that its existence is equivalent to the failure of the polarized relation( s ω) → ( s ω) 1,1 2. We show that the existence of a strong splitting family is consistent with ZFC, and that the strong splitting number equals the splitting number, when it exists. Consequently, we can put some restriction on the possibility that s is singular. In the second section we deal with the polarized relation under the weak diamond, and we prove that the strong polarized relation ω) → ( ω) 1,1 2 is consistent with ZFC, even when cf (2 ω1 (hence the weak diamond holds).

اللغة الأصليةإنجليزيّة أمريكيّة
الصفحات (من إلى)709-717
عدد الصفحات9
دوريةAnnals of Combinatorics
مستوى الصوت16
رقم الإصدار4
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - ديسمبر 2012

All Science Journal Classification (ASJC) codes

  • !!Discrete Mathematics and Combinatorics

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