Generic trees

Journal of Symbolic Logic 60 (3):705-726 (1995)
  Copy   BIBTEX

Abstract

We continue the investigation of the Laver ideal ℓ 0 and Miller ideal m 0 started in [GJSp] and [GRShSp]; these are the ideals on the Baire space associated with Laver forcing and Miller forcing. We solve several open problems from these papers. The main result is the construction of models for $t , where add denotes the additivity coefficient of an ideal. For this we construct amoeba forcings for these forcings which do not add Cohen reals. We show that c = ω 2 implies $\operatorname{add}(m^0) \leq \mathfrak{h}$ . We show that b = c, d = c implies $\operatorname{cov}(\ell^0) \leq \mathfrak{h}^+, \operatorname{cov}(m^0) \leq \mathfrak{h}^+$ respectively. Here $\operatorname{cov}$ denotes the covering coefficient. We also show that in the Cohen model $\operatorname{cov}(m^0) holds. Finally we prove that Cohen forcing does not add a superperfect tree of Cohen reals

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 89,446

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Unfoldable cardinals and the GCH.Joel David Hamkins - 2001 - Journal of Symbolic Logic 66 (3):1186-1198.
Cohen reals from small forcings.Janusz Pawlikowski - 2001 - Journal of Symbolic Logic 66 (1):318-324.
Classification and interpretation.Andreas Baudisch - 1989 - Journal of Symbolic Logic 54 (1):138-159.
Small forcings and Cohen reals.Jindřich Zapletal - 1997 - Journal of Symbolic Logic 62 (1):280-284.
Set theoretic properties of Loeb measure.Arnold W. Miller - 1990 - Journal of Symbolic Logic 55 (3):1022-1036.
Les automorphismes d'un ensemble fortement minimal.Daniel Lascar - 1992 - Journal of Symbolic Logic 57 (1):238-251.
Combinatorics on ideals and forcing with trees.Marcia J. Groszek - 1987 - Journal of Symbolic Logic 52 (3):582-593.

Analytics

Added to PP
2009-01-28

Downloads
203 (#87,880)

6 months
1 (#1,005,371)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Generalized Silver and Miller measurability.Giorgio Laguzzi - 2015 - Mathematical Logic Quarterly 61 (1-2):91-102.
Antichains of perfect and splitting trees.Paul Hein & Otmar Spinas - 2020 - Archive for Mathematical Logic 59 (3-4):367-388.
On the separation of regularity properties of the reals.Giorgio Laguzzi - 2014 - Archive for Mathematical Logic 53 (7-8):731-747.
Some considerations on amoeba forcing notions.Giorgio Laguzzi - 2014 - Archive for Mathematical Logic 53 (5-6):487-502.

View all 10 citations / Add more citations

References found in this work

Sacks forcing, Laver forcing, and Martin's axiom.Haim Judah, Arnold W. Miller & Saharon Shelah - 1992 - Archive for Mathematical Logic 31 (3):145-161.

Add more references