Concepedia

Ordinal Notation Systems

Ordinal Notation Systems is a formal framework in proof theory and mathematical logic that belongs to the class of symbolic systems used for representing ordinals, distinguished by its capacity to systematically assign notations to countable ordinals in a recursive manner, thereby enabling the analysis of transfinite induction and recursion within constructive mathematical frameworks.

19

Publications

1.6K

Citations

23

Authors

18

Institutions

Publications per year

2017–2026

0

Variants

Ordinal Notations

Parents

Publications

19

On notation for ordinal numbers

S. C. Kleene · Journal of Symbolic Logic · 1938 · 762 citations

, , +8

Recursive well-orderings

Clifford Spector · Journal of Symbolic Logic · 1955 · 212 citations

, , +16

Use of numerical symbols by the chimpanzee (Pan troglodytes): Cardinals, ordinals, and the introduction of zero

Dora Biro, Tetsuro Matsuzawa · Animal Cognition · 2001 · 164 citations

, , +10

Proof theory: the first step into impredicativity

Choice Reviews Online · 2009 · 86 citations

, , +15

Ordinal notations based on a weakly Mahlo cardinal

Michael Rathjen · Archive for Mathematical Logic · 1990 · 41 citations

, , +10

1–5 of 19

Authors

23

  1. WB
    Wilfried Buchholz

    Ludwig-Maximilians-Universität München, Germany

    2 publications · 41 citations

    2

    h-index

  2. TA
    Toshiyasu Arai

    Hiroshima University, Japan

    2 publications · 27 citations

    2

    h-index

  3. MR
    Michael Rathjen

    University of Leeds, United Kingdom

    2 publications · 70 citations

    2

    h-index

  4. WP
    Wolfram Pohlers

    Ludwig-Maximilians-Universität München, Germany

    2 publications · 41 citations

    2

    h-index

  5. LD
    Lev D. Beklemishev

    Steklov Mathematical Institute, Russia

    2 publications · 72 citations

    2

    h-index

1–5 of 23

Institutions

18

  1. The Ohio State University

    Columbus, United States

    3 h-index

    3 publications

    254 citations

  2. Ludwig-Maximilians-Universität München

    Munich, Germany

    2 h-index

    4 publications

    82 citations

  3. Hiroshima University

    Hiroshima, Japan

    1 h-index

    1 publications

    11 citations

  4. University of California System

    Oakland, United States

    1 h-index

    1 publications

    36 citations

  5. Oxford Research Group

    London, United Kingdom

    1 h-index

    1 publications

    164 citations

  6. University of Oxford

    Oxford, United Kingdom

    1 h-index

    1 publications

    164 citations

  7. Utrecht University

    Utrecht, The Netherlands

    1 h-index

    1 publications

    34 citations

  8. University of Latvia

    Riga, Latvia

    1 h-index

    1 publications

    15 citations

1–8 of 18

Venues

  1. Journal of Symbolic Logic

    10 publications · 1.1K citations

    10

    h-index

  2. Journal of Logic and Computation

    1 publications · 38 citations

    1

    h-index

  3. Mathematical logic quarterly

    MLQ · 1 publications · 29 citations

    1

    h-index

  4. Project Euclid (Cornell University)

    Repository · 1 publications · 19 citations

    1

    h-index

  5. Choice Reviews Online

    CRO · 1 publications · 86 citations

    1

    h-index

1–5