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1999 | 160 | 3 | 255-268
Tytuł artykułu

On absolutely divergent series

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We show that in the $ℵ_2$-stage countable support iteration of Mathias forcing over a model of CH the complete Boolean algebra generated by absolutely divergent series under eventual dominance is not isomorphic to the completion of P(ω)/fin. This complements Vojtáš' result that under $cf(\gc) = \gp$ the two algebras are isomorphic [15].
Słowa kluczowe
Rocznik
Tom
160
Numer
3
Strony
255-268
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-09-03
poprawiono
1999-03-18
Twórcy
  • Mathematisches Institut, Universität Bonn, Beringstr. 1 53115 Bonn, Germany, heike@math.uni-bonn.de
  • Mathematical Institute, The Hebrew University of Jerusalem, Givat Ram, 91904 Jerusalem, Israel
  • Mathematical Institute, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel, shelah@math.huji.ac.il
  • Mathematical Institute, Slovak Academy of Sciences, Jesenná 5, 04154 Košice, Slovak Republic, vojtas@kosice.upjs.sk
Bibliografia
  • [1] N. Alon, J. Spencer and P. Erdős, The Probabilistic Method, Wiley, 1992.
  • [2] B. Balcar, J. Pelant and P. Simon, The space of ultrafilters on N covered by nowhere dense sets, Fund. Math. 110 (1980), 11-24.
  • [3] T. Bartoszyński, Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), 209-213.
  • [4] T. Bartoszyński and M. Scheepers, Remarks on small sets related to trigonometric series, Topology Appl. 64 (1995), 133-140.
  • [5] J. Baumgartner, Iterated forcing, in: A. Mathias (ed.), Surveys in Set Theory, London Math. Soc. Lecture Note Ser. 8, Cambridge Univ. Press, 1983, 1-59.
  • [6] E. van Douwen, The integers and topology, in: K. Kunen and J. Vaughan (eds.), Handbook of Set-Theoretic Topology, North-Holland, 1984, 111-167.
  • [7] G. M. Fikhtengolz, Course of Differential and Integral Calculus, Nauka, Moscow, 1969 (in Russian).
  • [8] G. H. Hardy, Orders of Infinity. The 'Infinitärcalcül' of Paul du Bois Reymond, Cambridge Univ. Press, 1910.
  • [9] F. Hausdorff, Summen von $ℵ_1$ Mengen, Fund. Math. 26 (1936), 241-255.
  • [10] T. Jech, Set Theory, Addison-Wesley, 1978.
  • [11] T. Jech, Distributive laws, in: D. Monk (ed.), Handbook of Boolean Algebras, North-Holland, 1989, 317-332.
  • [12] K. Kunen, Set Theory. An Introduction to Independence Proofs, North-Holland, 1980.
  • [13] S. Shelah, Proper Forcing, Lecture Notes in Math. 940, Springer, 1982.
  • [14] S. Shelah and O. Spinas, The distributivity numbers of P(ω)/fin and its square, Trans. Amer. Math. Soc., to appear.
  • [15] P. Vojtáš, Boolean isomorphism between partial orderings of convergent and divergent series and infinite subsets of ℕ, Proc. Amer. Math. Soc. 117 (1993), 235-242.
  • [16] P. Vojtáš, On ω* and absolutely divergent series, Topology Proc. 19 (1994), 335-348.
  • </REFERENCES>
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv160i3p255bwm
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