Compactness of Powers of $ \omega $

Volume 61 / 2013

Paolo Lipparini Bulletin Polish Acad. Sci. Math. 61 (2013), 239-246 MSC: Primary 54B10, 54D20, 03C75; Secondary 03C20, 03E05, 54A20, 54A25. DOI: 10.4064/ba61-3-5


We characterize exactly the compactness properties of the product of $\kappa $ copies of the space $ \omega $ with the discrete topology. The characterization involves uniform ultrafilters, infinitary languages, and the existence of nonstandard elements in elementary extensions. We also have results involving products of possibly uncountable regular cardinals.


  • Paolo LippariniDipartimento di Matematica
    II Università di Roma (Tor Vergata)
    Viale della Ricerca Scientifica
    I-00133 Roma, Italy

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