Preserving old ([omega]^{aleph_0},supseteq^*) is proper
Saharon Shelah
TL;DR
This paper investigates conditions under which certain forcing notions preserve the properness of the partial order of countably infinite subsets of omega, providing a comprehensive set of criteria applicable to many forcing notions.
Contribution
It establishes both necessary and sufficient conditions for a forcing notion to preserve the properness of ([omega]^{aleph_0},supseteq^*), expanding understanding of properness preservation.
Findings
Identifies conditions that ensure preservation of properness.
Covers a wide range of forcing notions.
Provides a unified framework for properness preservation.
Abstract
We give some sufficient and necessary conditions on a forcing notion Q for preserving the forcing notion ([omega]^{aleph_0},supseteq^*) is proper. They cover many reasonable forcing notions.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Rings, Modules, and Algebras