# The distributivity numbers of finite products of P(ω)/fin

Fundamenta Mathematicae (1998)

- Volume: 158, Issue: 1, page 81-93
- ISSN: 0016-2736

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topShelah, Saharon, and Spinas, Otmar. "The distributivity numbers of finite products of P(ω)/fin." Fundamenta Mathematicae 158.1 (1998): 81-93. <http://eudml.org/doc/212304>.

@article{Shelah1998,

abstract = {Generalizing [ShSp], for every n < ω we construct a ZFC-model where ℌ(n), the distributivity number of r.o.$(P(ω)/fin)^n$, is greater than ℌ(n+1). This answers an old problem of Balcar, Pelant and Simon (see [BaPeSi]). We also show that both Laver and Miller forcings collapse the continuum to ℌ(n) for every n < ω, hence by the first result, consistently they collapse it below ℌ(n).},

author = {Shelah, Saharon, Spinas, Otmar},

journal = {Fundamenta Mathematicae},

keywords = {forcing; Boolean algebras},

language = {eng},

number = {1},

pages = {81-93},

title = {The distributivity numbers of finite products of P(ω)/fin},

url = {http://eudml.org/doc/212304},

volume = {158},

year = {1998},

}

TY - JOUR

AU - Shelah, Saharon

AU - Spinas, Otmar

TI - The distributivity numbers of finite products of P(ω)/fin

JO - Fundamenta Mathematicae

PY - 1998

VL - 158

IS - 1

SP - 81

EP - 93

AB - Generalizing [ShSp], for every n < ω we construct a ZFC-model where ℌ(n), the distributivity number of r.o.$(P(ω)/fin)^n$, is greater than ℌ(n+1). This answers an old problem of Balcar, Pelant and Simon (see [BaPeSi]). We also show that both Laver and Miller forcings collapse the continuum to ℌ(n) for every n < ω, hence by the first result, consistently they collapse it below ℌ(n).

LA - eng

KW - forcing; Boolean algebras

UR - http://eudml.org/doc/212304

ER -

## References

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- [Go] M. Goldstern, Tools for your forcing construction, in: Israel Math. Conf. Proc. 6, H. Judah (ed.), Bar-Han Univ., Ramat Gan, 1993, 305-360. Zbl0834.03016
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- [GoReShSp] M. Goldstern, M. Repický, S. Shelah and O. Spinas, On tree ideals, ibid. 123 (1995), 1573-1581. Zbl0823.03027
- [JuSh] H. Judah and S. Shelah, Souslin forcing, J. Symbolic Logic 53 (1988), 1188-1207.
- [Mt] A. R. D. Mathias, Happy families, Ann. Math. Logic 12 (1977), 59-111.
- [Shb] S. Shelah, Proper Forcing, Lecture Notes in Math. 940, Springer, 1982.
- [ShSp] S. Shelah and O. Spinas, The distributivity number of P(ω)/fin and its square, Trans. Amer. Math. Soc., to appear.

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