Concepedia

Simple Sets

Simple Set is a recursively enumerable set whose complement is infinite but contains no infinite recursively enumerable subset, thereby distinguishing it within the class of recursively enumerable sets by exhibiting a minimal form of non-computability.

85

Publications

3K

Citations

146

Authors

103

Institutions

Publications per year

2017–2026

4

Parents

Publications

85

Fault diagnosis and fault tolerant control using set-membership approaches: Application to real case studies

Vicenç Puig · International Journal of Applied Mathematics and Computer Science · 2010 · 176 citations · Full text

, , +13

The Classification of the Finite Simple Groups

Michael Aschbacher · The Mathematical Intelligencer · 1980 · 174 citations

, , +6

On the lattice of recursively enumerable sets

A. H. Lachlan · Transactions of the American Mathematical Society · 1968 · 149 citations

, , +15

An algebraic decomposition of the recursively enumerable degrees and the coincidence of several degree classes with the promptly simple degrees

Klaus Ambos‐Spies, Carl G. Jockusch, Richard A. Shore et al. · Transactions of the American Mathematical Society · 1984 · 98 citations · Full text

, , +13

Using random sets as oracles

Denis R. Hirschfeldt, André Nies, Frank Stephan · Journal of the London Mathematical Society · 2007 · 91 citations

, , +10

1–5 of 85

Authors

146

  1. RI
    Robert I. Soare

    University of Chicago, United States

    4 publications · 161 citations

    4

    h-index

  2. CG
    Carl G. Jockusch

    University of Illinois Urbana-Champaign, United States

    3 publications · 124 citations

    3

    h-index

  3. RA
    Richard A. Shore

    Cornell University, United States

    3 publications · 147 citations

    3

    h-index

  4. JL
    José L. Balcázar

    Universitat Politècnica de Catalunya, Spain

    2 publications · 46 citations

    2

    h-index

  5. DA
    Donald A. Martin

    University of California, Los Angeles, United States

    2 publications · 71 citations

    2

    h-index

1–5 of 146

Institutions

103

  1. University of Chicago

    Chicago, United States

    5 h-index

    11 publications

    595 citations

  2. Cornell University

    Ithaca, United States

    4 h-index

    10 publications

    513 citations

  3. University of Wisconsin–Madison

    Madison, United States

    4 h-index

    8 publications

    173 citations

  4. Massachusetts Institute of Technology

    Cambridge, United States

    3 h-index

    3 publications

    106 citations

  5. Victoria University of Wellington

    Wellington, New Zealand

    3 h-index

    8 publications

    153 citations

  6. Universitat Politècnica de Catalunya

    Barcelona, Spain

    3 h-index

    3 publications

    206 citations

  7. University of Illinois Urbana-Champaign

    Urbana, United States

    3 h-index

    10 publications

    508 citations

  8. Centre National de la Recherche Scientifique

    Paris, France

    3 h-index

    5 publications

    82 citations

1–8 of 103

Venues

  1. Journal of Symbolic Logic

    13 publications · 392 citations

    12

    h-index

  2. Transactions of the American Mathematical Society

    TRAN · 7 publications · 392 citations

    7

    h-index

  3. Theoretical Computer Science

    4 publications · 123 citations

    4

    h-index

  4. Proceedings of the American Mathematical Society

    PROC · 3 publications · 65 citations

    3

    h-index

  5. Pacific Journal of Mathematics

    3 publications · 80 citations

    3

    h-index

1–5