# On absolutely divergent series

Sakaé Fuchino; Heike Mildenberger; Saharon Shelah; Peter Vojtáš

Fundamenta Mathematicae (1999)

- Volume: 160, Issue: 3, page 255-268
- ISSN: 0016-2736

## Access Full Article

top## Abstract

top## How to cite

topFuchino, Sakaé, et al. "On absolutely divergent series." Fundamenta Mathematicae 160.3 (1999): 255-268. <http://eudml.org/doc/212392>.

@article{Fuchino1999,

abstract = {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() = $ the two algebras are isomorphic [15].},

author = {Fuchino, Sakaé, Mildenberger, Heike, Shelah, Saharon, Vojtáš, Peter},

journal = {Fundamenta Mathematicae},

keywords = {-distributive Boolean algebra; Mathias forcing; absolutely divergent series; factor algebra of the power set algebra},

language = {eng},

number = {3},

pages = {255-268},

title = {On absolutely divergent series},

url = {http://eudml.org/doc/212392},

volume = {160},

year = {1999},

}

TY - JOUR

AU - Fuchino, Sakaé

AU - Mildenberger, Heike

AU - Shelah, Saharon

AU - Vojtáš, Peter

TI - On absolutely divergent series

JO - Fundamenta Mathematicae

PY - 1999

VL - 160

IS - 3

SP - 255

EP - 268

AB - 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() = $ the two algebras are isomorphic [15].

LA - eng

KW - -distributive Boolean algebra; Mathias forcing; absolutely divergent series; factor algebra of the power set algebra

UR - http://eudml.org/doc/212392

ER -

## References

top- [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. Zbl0568.54004
- [3] T. Bartoszyński, Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), 209-213. Zbl0538.03042
- [4] T. Bartoszyński and M. Scheepers, Remarks on small sets related to trigonometric series, Topology Appl. 64 (1995), 133-140. Zbl0828.42004
- [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. Zbl0524.03040
- [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. Zbl41.0303.01
- [9] F. Hausdorff, Summen von ${\aleph}_{1}$ 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. Zbl0943.03036
- [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. Zbl0765.03023
- [16] P. Vojtáš, On ω* and absolutely divergent series, Topology Proc. 19 (1994), 335-348. Zbl0840.03033
- </REFERENCES>

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.