Concepedia

Ultrafilter Lemma

The Ultrafilter Lemma is a foundational principle in set theory stating that every proper filter on a non-empty set can be extended to an ultrafilter, distinguishing it within the class of choice principles by being strictly weaker than the Axiom of Choice yet sufficient for many compactness and model-theoretic arguments.

46

Publications

1.2K

Citations

59

Authors

45

Institutions

Publications per year

2017–2026

7

Variants

Ultrafilter Theorem

Parents

Publications

46

Ultraproducts and elementary classes

H. Jerome Keisler · Indagationes Mathematicae (Proceedings) · 1961 · 142 citations

, , +2

Ultrafilters and compactification of uniform spaces

Transactions of the American Mathematical Society · 1948 · 101 citations · Full text

, , +7

On cardinalities of ultraproducts

H. Jerome Keisler · Bulletin of the American Mathematical Society · 1964 · 54 citations · Full text

, , +3

On well-filtered spaces and ordered sets

Xiaoyong Xi, Jimmie Lawson · Topology and its Applications · 2017 · 51 citations

, , +7

Universal properties of L(F∞) in subfactor theory

Sorin Popa, Dimitri Shlyakhtenko · Acta Mathematica · 2003 · 48 citations · Full text

, , +3

1–5 of 46

Authors

59

  1. XX
    Xiaoyong Xi

    Jiangsu Normal University, China

    4 publications · 103 citations

    4

    h-index

  2. SS
    Saharon Shelah

    Hebrew University of Jerusalem, Israel

    3 publications · 65 citations

    3

    h-index

  3. DZ
    Dongsheng Zhao

    Nanyang Technological University, Singapore

    2 publications · 34 citations

    2

    h-index

  4. HJ
    H. Jerome Keisler

    University of Wisconsin–Madison, United States

    2 publications · 196 citations

    2

    h-index

  5. GW
    Guohua Wu

    Central South University, China

    2 publications · 32 citations

    2

    h-index

1–5 of 59

Institutions

45

  1. Hebrew University of Jerusalem

    Jerusalem, Israel

    4 h-index

    6 publications

    84 citations

  2. Minnan Normal University

    Zhangzhou, China

    2 h-index

    2 publications

    34 citations

  3. Nanyang Technological University

    Singapore, Singapore

    2 h-index

    4 publications

    62 citations

  4. University of Vienna

    Vienna, Austria

    2 h-index

    2 publications

    52 citations

  5. Union College

    Schenectady, United States

    2 h-index

    3 publications

    51 citations

  6. Jiangsu Normal University

    Xuzhou, China

    2 h-index

    2 publications

    71 citations

  7. Nanjing Normal University

    Nanjing, China

    1 h-index

    1 publications

    20 citations

  8. Laboratoire de Géologie de l’École Normale Supérieure

    Paris, France

    1 h-index

    1 publications

    10 citations

1–8 of 45

Venues

  1. Topology and its Applications

    6 publications · 154 citations

    6

    h-index

  2. Transactions of the American Mathematical Society

    TRAN · 5 publications · 207 citations

    5

    h-index

  3. Annals of Pure and Applied Logic

    3 publications · 58 citations

    3

    h-index

  4. Israel Journal of Mathematics

    3 publications · 48 citations

    3

    h-index

  5. Journal of Symbolic Logic

    3 publications · 82 citations

    3

    h-index

1–5