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Generic trees

Published online by Cambridge University Press:  12 March 2014

Otmar Spinas
Otmar Spinas*
Affiliation:
Mathematik Eth-Zentrum, 8092 Zürich, Switzerland Institute of Mathematics, The Hebrew University, Givat Ram, 91904 Jerusalem, Israel
*
Department of Mathematics, University of California, Irvine, California 92717, E-mail: ospinas@math.uci.edu
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Abstract

We continue the investigation of the Laver ideal ℓ0 and Miller ideal m0 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 < add(ℓ0), < add(m0), 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 = ω2 implies add(m0) ≤ . We show that , implies cov(ℓ0) ≤ +, cov(m0) ≤ + respectively. Here cov denotes the covering coefficient. We also show that in the Cohen model cov(m0) < holds. Finally we prove that Cohen forcing does not add a superperfect tree of Cohen reals.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 3 , September 1995 , pp. 705 - 726
Copyright
Copyright © Association for Symbolic Logic 1995

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