Concepedia

Cardinal Arithmetic

Cardinal Arithmetic is a branch of set theory that studies the operations and rules governing the addition, multiplication, and exponentiation of cardinal numbers, distinguishing itself by focusing on the quantitative properties of infinite sets under these operations.

437

Publications

17.4K

Citations

460

Authors

261

Institutions

Publications per year

2017–2026

30

Parents

Children

Publications

437

The Foundations of Arithmetic. A Logico-Mathematical Enquiry into the Concept of Number.

E. N., Gottlob Frege, J. L. Austin · The Journal of Philosophy · 1951 · 630 citations

, , +16

Five short stories about the cardinal series

John R. Higgins · Bulletin of the American Mathematical Society · 1985 · 381 citations · Full text

, , +4

Martin's Maximum, Saturated Ideals, and Non-Regular Ultrafilters. Part I

M. Foreman, M. Magidor, Saharon Shelah · Annals of Mathematics · 1988 · 362 citations

, , +7

Contributions to the Founding of the Theory of Transfinite Numbers.

Cassius J. Keyser, Georg Cantor, Philip E. B. Jourdain · The Journal of Philosophy Psychology and Scientific Methods · 1916 · 343 citations

, , +1

The higher infinite: large cardinals in set theory from their beginnings

Choice Reviews Online · 1996 · 324 citations

, , +15

1–5 of 437

Authors

460

  1. SS
    Saharon Shelah

    Hebrew University of Jerusalem, Israel

    43 publications · 1.8K citations

    24

    h-index

  2. AW
    Arthur W. Apter

    Baruch College, United States

    9 publications · 151 citations

    9

    h-index

  3. MG
    Moti Gitik

    Tel Aviv University, Israel

    8 publications · 303 citations

    8

    h-index

  4. JC
    James Cummings

    Carnegie Mellon University, United States

    7 publications · 432 citations

    7

    h-index

  5. JB
    Jörg Brendle

    Kobe University, Japan

    7 publications · 128 citations

    7

    h-index

1–5 of 460

Institutions

261

  1. Hebrew University of Jerusalem

    Jerusalem, Israel

    22 h-index

    45 publications

    1.7K citations

  2. University of California, Berkeley

    Berkeley, United States

    14 h-index

    16 publications

    563 citations

  3. Rutgers, The State University of New Jersey

    New Brunswick, United States

    13 h-index

    21 publications

    433 citations

  4. Universitat de Barcelona

    Barcelona, Spain

    9 h-index

    9 publications

    224 citations

  5. Tel Aviv University

    Tel Aviv, Israel

    9 h-index

    10 publications

    336 citations

  6. The Ohio State University

    Columbus, United States

    8 h-index

    8 publications

    178 citations

  7. University of California, Los Angeles

    Los Angeles, United States

    7 h-index

    8 publications

    183 citations

  8. Carnegie Mellon University

    Pittsburgh, United States

    6 h-index

    6 publications

    375 citations

1–8 of 261

Venues

  1. Journal of Symbolic Logic

    45 publications · 1.2K citations

    21

    h-index

  2. Annals of Pure and Applied Logic

    30 publications · 873 citations

    18

    h-index

  3. Fundamenta Mathematicae

    26 publications · 926 citations

    17

    h-index

  4. Israel Journal of Mathematics

    13 publications · 453 citations

    12

    h-index

  5. American Mathematical Monthly

    13 publications · 857 citations

    12

    h-index

1–5