Forking in NTP_2 theories
Artem Chernikov, Itay Kaplan
TL;DR
This paper proves that in NTP_2 theories, forking and dividing coincide over models and extension bases, and dependence is characterized by bounded non-forking.
Contribution
It establishes the equivalence of forking and dividing over models in NTP_2 theories and links dependence to bounded non-forking.
Findings
Forking and dividing are the same over models in NTP_2 theories.
Dependence is equivalent to bounded non-forking in NTP_2 theories.
Results apply to dependent and simple theories.
Abstract
We prove that in theories without the tree property of the second kind (which include dependent and simple theories) forking and dividing over models are the same, and in fact over any extension base. As an application we show that dependence is equivalent to bounded non-forking assuming NTP_2.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Logic, Reasoning, and Knowledge · Logic, programming, and type systems