Forcing absoluteness and regularity properties

Annals of Pure and Applied Logic 161 (7):879-894 (2010)
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Abstract

For a large natural class of forcing notions, we prove general equivalence theorems between forcing absoluteness statements, regularity properties, and transcendence properties over and the core model . We use our results to answer open questions from set theory of the reals

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10.1016/j.apal.2009.10.005

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Citations of this work

Regularity properties on the generalized reals.Sy David Friedman, Yurii Khomskii & Vadim Kulikov - 2016 - Annals of Pure and Applied Logic 167 (4):408-430.
Full-splitting Miller trees and infinitely often equal reals.Yurii Khomskii & Giorgio Laguzzi - 2017 - Annals of Pure and Applied Logic 168 (8):1491-1506.
On the separation of regularity properties of the reals.Giorgio Laguzzi - 2014 - Archive for Mathematical Logic 53 (7-8):731-747.

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References found in this work

The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
The core model.A. Dodd & R. Jensen - 1981 - Annals of Mathematical Logic 20 (1):43-75.
Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.
Δ12-sets of reals.Jaime I. Ihoda & Saharon Shelah - 1989 - Annals of Pure and Applied Logic 42 (3):207-223.
Solovay-Type Characterizations for Forcing-Algebras.Jörg Brendle & Benedikt Löwe - 1999 - Journal of Symbolic Logic 64 (3):1307-1323.

View all 15 references / Add more references