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The relationships among many notions of largeness for subsets of a semigroup

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Abstract

We deal with 26 notions of largeness in a semigroup. These notions have their origins in topological dynamics and the algebraic theory of Stone–Čech compactifications, mostly as applied to Ramsey Theory. We establish exactly the patterns of implications that must hold among 24 of these. We also note which of them are partition regular in the sense that whenever the union of two sets is large, one of them must be large.

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Authors and Affiliations

  1. Department of Mathematics, Howard University, Washington, DC, 20059, USA

    Neil Hindman

  2. Department of Mathematics and Statistics, University of Arkansas, Little Rock, AR, 72204, USA

    Lakeshia Legette Jones

  3. Department of Pure Mathematics, University of Leeds, Leeds, LS2 9J2, UK

    Dona Strauss

Authors
  1. Neil Hindman
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  2. Lakeshia Legette Jones
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  3. Dona Strauss
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Corresponding author

Correspondence to Lakeshia Legette Jones.

Additional information

Communicated by Jimmie D. Lawson.

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Hindman, N., Jones, L.L. & Strauss, D. The relationships among many notions of largeness for subsets of a semigroup. Semigroup Forum 99, 9–31 (2019). https://doi.org/10.1007/s00233-018-9944-3

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  • DOI: https://doi.org/10.1007/s00233-018-9944-3

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