Ultrafilters in reverse mathematics

被引：4
|
作者：
Towsner, Henry [1 ]
机构：
[1] Univ Penn, Dept Math, Philadelphia, PA 19104 USA
来源：
JOURNAL OF MATHEMATICAL LOGIC | 2014年 / 14卷 / 01期
基金：
美国国家科学基金会;
关键词：
Reverse mathematics; ultrafilters; forcing; conservative; HINDMANS THEOREM; PROOF;
D O I：
10.1142/S0219061314500019
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We extend theories of reverse mathematics by a non-principal ultrafilter, and show that these are conservative extensions of the usual theories ACA(0), ATR(0), and Pi(1)(1)-CA(0).
引用
收藏
页数：11
相关论文
共 50 条
  • [41] Reverse mathematics and initial intervals
    Frittaion, Emanuele
    Marcone, Alberto
    [J]. ANNALS OF PURE AND APPLIED LOGIC, 2014, 165 (03) : 858 - 879
  • [42] Splittings and Disjunctions in Reverse Mathematics
    Sanders, Sam
    [J]. NOTRE DAME JOURNAL OF FORMAL LOGIC, 2020, 61 (01) : 51 - 74
  • [43] ON STRONGLY SUMMABLE ULTRAFILTERS AND UNION ULTRAFILTERS
    BLASS, A
    HINDMAN, N
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 304 (01) : 83 - 99
  • [44] REVERSE MATHEMATICS, COMPUTABILITY, AND PARTITIONS OF TREES
    Chubb, Jennifer
    Hirst, Jeffry L.
    Mcnicholl, Timothy H.
    [J]. JOURNAL OF SYMBOLIC LOGIC, 2009, 74 (01) : 201 - 215
  • [45] TRANSFINITE RECURSION IN HIGHER REVERSE MATHEMATICS
    Schweber, Noah
    [J]. JOURNAL OF SYMBOLIC LOGIC, 2015, 80 (03) : 940 - 969
  • [46] Reverse mathematics of prime factorization of ordinals
    Hirst, JL
    [J]. ARCHIVE FOR MATHEMATICAL LOGIC, 1999, 38 (03) : 195 - 201
  • [47] Whitehead’s problem and reverse mathematics
    Yang Sen
    [J]. Israel Journal of Mathematics, 2018, 228 : 455 - 512
  • [48] Ultrafilters
    Di Nasso, Mauro
    Goldbring, Isaac
    Lupini, Martino
    [J]. NONSTANDARD METHODS IN RAMSEY THEORY AND COMBINATORIAL NUMBER THEORY, 2019, 2239 : 3 - 10
  • [49] Ultrafilters
    Komjath, Peter
    Totik, Vilmos
    [J]. AMERICAN MATHEMATICAL MONTHLY, 2008, 115 (01): : 33 - 44
  • [50] THE REVERSE MATHEMATICS OF THE TIETZE EXTENSION THEOREM
    Shafer, Paul
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (12) : 5359 - 5370
12345