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We characterize exactly the compactness properties of the product of κ copies of the space ω 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 Lipparini. "Compactness of Powers of ω." Bulletin of the Polish Academy of Sciences. Mathematics 61.3 (2013): 239-246. <http://eudml.org/doc/281336>.
@article{PaoloLipparini2013, abstract = {We characterize exactly the compactness properties of the product of κ copies of the space ω 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.}, author = {Paolo Lipparini}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, keywords = {powers of omega; (finally) compact topological space; infinitary language; ultrafilter convergence; uniform ultrafilter; -nonstandard element; weakly compact cardinal}, language = {eng}, number = {3}, pages = {239-246}, title = {Compactness of Powers of ω}, url = {http://eudml.org/doc/281336}, volume = {61}, year = {2013}, }
TY - JOUR AU - Paolo Lipparini TI - Compactness of Powers of ω JO - Bulletin of the Polish Academy of Sciences. Mathematics PY - 2013 VL - 61 IS - 3 SP - 239 EP - 246 AB - We characterize exactly the compactness properties of the product of κ copies of the space ω 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. LA - eng KW - powers of omega; (finally) compact topological space; infinitary language; ultrafilter convergence; uniform ultrafilter; -nonstandard element; weakly compact cardinal UR - http://eudml.org/doc/281336 ER -