کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4665612 1633819 2015 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Splitting families of sets in ZFC
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Splitting families of sets in ZFC
چکیده انگلیسی

Miller's 1937 splitting theorem was proved for every finite n>0n>0 for all ρ-uniform families of sets in which ρ is infinite. A simple method for proving Miller-type splitting theorems is presented here and an extension of Miller's theorem is proved in ZFC for every cardinal ν for all ρ  -uniform families in which ρ≥ℶω(ν)ρ≥ℶω(ν). The main ingredient in the method is an asymptotic infinitary Löwenheim–Skolem theorem for anti-monotone set functions.As corollaries, the use of additional axioms is eliminated from splitting theorems due to Erdős and Hajnal [1], Komjáth [7], Hajnal, Juhász and Shelah [4]; upper bounds are set on conflict-free coloring numbers of families of sets; and a general comparison theorem for ρ  -uniform families of sets is proved, which generalizes Komjáth's comparison theorem for ℵ0ℵ0-uniform families [8].

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 269, 10 January 2015, Pages 707–725
نویسندگان
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