Transcendental pairs of generic extensions
Jindrich Zapletal
TL;DR
This paper introduces a new class of Suslin forcings that preserve certain properties and demonstrates their implications for the consistency of countable chromatic numbers in Borel hypergraphs within ZF+DC.
Contribution
It identifies a novel preservation class of Suslin forcings and explores their consequences in the choiceless set theory context.
Findings
Established a new preservation class of Suslin forcings.
Proved consistency results for countable chromatic numbers in Borel hypergraphs.
Extended results to ZF+DC without the Axiom of Choice.
Abstract
We isolate a new preservation class of Suslin forcings and prove several associated consistency results in the choiceless theory ZF+DC regarding countable chromatic numbers of various Borel hypergraphs.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Limits and Structures in Graph Theory