Concepedia

Ordinal Arithmetic

Ordinal Arithmetic is a formal system within set theory that extends the operations of addition, multiplication, and exponentiation to ordinal numbers, distinguished by its recursive definitions based on transfinite induction and its non-commutative behavior under these operations.

91

Publications

4.4K

Citations

143

Authors

97

Institutions

Publications per year

2017–2026

9

Parents

Publications

91

Can Likert Scales be Treated as Interval Scales?—A Simulation Study

Huiping Wu, Shing-On Leung · Journal of Social Service Research · 2017 · 525 citations

, , +11

Avoiding Power Loss Associated with Categorization and Ordinal Scores in Dose-Response and Trend Analysis

Sander Greenland · Epidemiology · 1995 · 362 citations

, , +13

Archimedean overlap functions: The ordinal sum and the cancellation, idempotency and limiting properties

Graçaliz Pereira Dimuro, Benjamín Bedregal · Fuzzy Sets and Systems · 2014 · 168 citations

, , +11

Inconsistent models of arithmetic Part II: the general case

Graham Priest · Journal of Symbolic Logic · 2000 · 136 citations

, , +11

The ordinal consistency of a fuzzy preference relation

Yejun Xu, Ravi Patnayakuni, Huimin Wang · Information Sciences · 2012 · 129 citations

, , +13

1–5 of 91

Authors

143

  1. GT
    Gaisi Takeuti

    University of Illinois Urbana-Champaign, United States

    5 publications · 108 citations

    5

    h-index

  2. RS
    Richard Sommer

    Stanford University, United States

    3 publications · 71 citations

    3

    h-index

  3. GW
    Gunnar Wilken

    The Ohio State University, United States

    3 publications · 39 citations

    3

    h-index

  4. SC
    S. C. Kleene

    University of Wisconsin–Madison, United States

    3 publications · 345 citations

    3

    h-index

  5. MR
    Michael Rathjen

    University of Leeds, United Kingdom

    3 publications · 136 citations

    3

    h-index

1–5 of 143

Institutions

97

  1. The Ohio State University

    Columbus, United States

    4 h-index

    4 publications

    59 citations

  2. Stanford University

    Stanford, United States

    4 h-index

    4 publications

    128 citations

  3. University of California, Los Angeles

    Los Angeles, United States

    3 h-index

    3 publications

    146 citations

  4. University of Education, Winneba

    Winneba, Ghana

    3 h-index

    4 publications

    73 citations

  5. University of Oxford

    Oxford, United Kingdom

    2 h-index

    2 publications

    78 citations

  6. University of Bonn

    Bonn, Germany

    2 h-index

    3 publications

    124 citations

  7. Shandong University

    Jinan, China

    2 h-index

    4 publications

    229 citations

  8. University of Bern

    Bern, Switzerland

    2 h-index

    4 publications

    54 citations

1–8 of 97

Venues

  1. Journal of Symbolic Logic

    13 publications · 510 citations

    11

    h-index

  2. Annals of Pure and Applied Logic

    7 publications · 360 citations

    7

    h-index

  3. Archive for Mathematical Logic

    5 publications · 136 citations

    5

    h-index

  4. Journal of the Mathematical Society of Japan

    4 publications · 80 citations

    4

    h-index

  5. Fuzzy Sets and Systems

    4 publications · 289 citations

    4

    h-index

1–5