Definability of types over finite partial order indiscernibles
Vincent Guingona
TL;DR
This paper characterizes dependent formulas via uniform definability of types over finite partial order indiscernibles, extending previous results through a decomposition of truth values for externally definable formulas.
Contribution
It generalizes the characterization of dependence to finite partial order indiscernibles, providing a new decomposition method for truth values.
Findings
Dependent formulas are characterized by uniform definability over finite partial order indiscernibles
Provides a decomposition of truth values for externally definable formulas
Extends previous results to a broader class of indiscernibles
Abstract
In this paper, we show that a partitioned formula \phi is dependent if and only if \phi has uniform definability of types over finite partial order indiscernibles. This generalizes our result from a previous paper [1]. We show this by giving a decomposition of the truth values of an externally definable formula on a finite partial order indiscernible.
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Taxonomy
TopicsAdvanced Algebra and Logic · Computability, Logic, AI Algorithms · Advanced Topology and Set Theory