Concepedia

Hyperarithmetical Hierarchy

The Hyperarithmetical Hierarchy is a stratification of sets of natural numbers, ordered by definability through iterated jump operators along recursive ordinals, that extends the arithmetical hierarchy by allowing transfinite levels via recursive well-orderings in the context of effective descriptive set theory.

24

Publications

1.2K

Citations

24

Authors

19

Institutions

Publications per year

2017–2026

0

Parents

Publications

24

Recursive well-orderings

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

, , +16

Recursive pseudo-well-orderings

Transactions of the American Mathematical Society · 1968 · 119 citations · Full text

, , +12

Recursive labelling systems and stability of recursive structures in hyperarithmetical degrees

C. J. Ash · Transactions of the American Mathematical Society · 1986 · 100 citations · Full text

, , +13

Pseudo-jump operators. II: Transfinite iterations, hierarchies and minimal covers

Carl G. Jockusch, Richard A. Shore · Journal of Symbolic Logic · 1984 · 92 citations

, , +14

The next admissible set

K. Jon Barwise, R. O. Gandy, Yiannis N. Moschovakis · Journal of Symbolic Logic · 1971 · 66 citations

, , +10

1–5 of 24

Authors

24

  1. CJ
    C. J. Ash

    Monash University, Australia

    3 publications · 172 citations

    3

    h-index

  2. HF
    Harvey Friedman

    University at Buffalo, State University of New York, United States

    2 publications · 55 citations

    2

    h-index

  3. YN
    Yiannis N. Moschovakis

    University of California, Los Angeles, United States

    2 publications · 87 citations

    2

    h-index

  4. VS
    Victor Selivanov

    Russian Academy of Sciences, Russia

    2 publications · 38 citations

    2

    h-index

  5. GE
    Gerald E. Sacks

    Massachusetts Institute of Technology, United States

    2 publications · 66 citations

    2

    h-index

1–5 of 24

Institutions

19

  1. University of Notre Dame

    Notre Dame, United States

    3 h-index

    4 publications

    110 citations

  2. Monash University

    Melbourne, Australia

    3 h-index

    3 publications

    172 citations

  3. University of California System

    Oakland, United States

    2 h-index

    2 publications

    102 citations

  4. The Ohio State University

    Columbus, United States

    2 h-index

    2 publications

    245 citations

  5. University at Buffalo, State University of New York

    Buffalo, United States

    2 h-index

    2 publications

    55 citations

  6. Cornell University

    Ithaca, United States

    2 h-index

    5 publications

    379 citations

  7. University of California, Los Angeles

    Los Angeles, United States

    2 h-index

    2 publications

    102 citations

  8. University of Wisconsin–Madison

    Madison, United States

    1 h-index

    1 publications

    66 citations

1–8 of 19

Venues

  1. Transactions of the American Mathematical Society

    TRAN · 8 publications · 351 citations

    8

    h-index

  2. Journal of Symbolic Logic

    8 publications · 527 citations

    8

    h-index

  3. Notre Dame Journal of Formal Logic

    2 publications · 88 citations

    2

    h-index

  4. Journal of Mathematical Logic

    1 publications · 31 citations

    1

    h-index

  5. Proceedings of the American Mathematical Society

    PROC · 1 publications · 20 citations

    1

    h-index

1–5