## Proper products

HTML articles powered by AMS MathViewer

- by Otmar Spinas PDF
- Proc. Amer. Math. Soc.
**137**(2009), 2767-2772 Request permission

## Abstract:

We show that the natural amoeba forcing associated with Laver forcing $\mathbb {L}$, Miller forcing $\mathbb {M}$ respectively, is proper. As a corollary we obtain that every finite power of $\mathbb {L}$, respectively $\mathbb {M}$, is proper.## References

- James E. Baumgartner,
*Iterated forcing*, Surveys in set theory, London Math. Soc. Lecture Note Ser., vol. 87, Cambridge Univ. Press, Cambridge, 1983, pp. 1–59. MR**823775**, DOI 10.1017/CBO9780511758867.002 - J. Brendle,
*Mutual generics and perfect free subsets*, Acta Math. Hungar.**82**(1999), no. 1-2, 143–161. MR**1658566**, DOI 10.1023/A:1026458210592 - Richard Laver,
*On the consistency of Borel’s conjecture*, Acta Math.**137**(1976), no. 3-4, 151–169. MR**422027**, DOI 10.1007/BF02392416 - Arnold W. Miller,
*Rational perfect set forcing*, Axiomatic set theory (Boulder, Colo., 1983) Contemp. Math., vol. 31, Amer. Math. Soc., Providence, RI, 1984, pp. 143–159. MR**763899**, DOI 10.1090/conm/031/763899 - Saharon Shelah,
*Proper forcing*, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin-New York, 1982. MR**675955** - Saharon Shelah and Otmar Spinas,
*The distributivity numbers of finite products of ${\scr P}(\omega )/\rm fin$*, Fund. Math.**158**(1998), no. 1, 81–93. MR**1641157** - Otmar Spinas,
*Generic trees*, J. Symbolic Logic**60**(1995), no. 3, 705–726. MR**1348990**, DOI 10.2307/2275753 - Otmar Spinas,
*Ramsey and freeness properties of Polish planes*, Proc. London Math. Soc. (3)**82**(2001), no. 1, 31–63. MR**1794256**, DOI 10.1112/S0024611500012740 - Boban Velickovic and W. Hugh Woodin,
*Complexity of reals in inner models of set theory*, Ann. Pure Appl. Logic**92**(1998), no. 3, 283–295. MR**1640916**, DOI 10.1016/S0168-0072(98)00010-4

## Additional Information

**Otmar Spinas**- Affiliation: Mathematisches Seminar der Christian-Albrechts-Universität zu Kiel, Ludewig- Meyn-Straße 4, 24098 Kiel, Germany
- Email: spinas@math.uni-kiel.de
- Received by editor(s): December 10, 2007
- Received by editor(s) in revised form: March 28, 2008, and December 5, 2008
- Published electronically: March 5, 2009
- Additional Notes: The author is partially supported by DFG grant SP 683/1-2
- Communicated by: Julia Knight
- © Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**137**(2009), 2767-2772 - MSC (2000): Primary 03E05
- DOI: https://doi.org/10.1090/S0002-9939-09-09846-3
- MathSciNet review: 2497491