On stable fields and weight
Krzysztof Krupinski, Anand Pillay
TL;DR
This paper proves that infinite stable fields with a generic type of weight 1 are separably closed, and explores related properties for fields with finite weight or strong stability.
Contribution
It establishes that infinite stable fields with generic weight 1 are separably closed and provides partial results for fields with finite weight or strong stability.
Findings
Infinite stable fields with generic weight 1 are separably closed
Partial results for fields with finite weight
Results for strongly stable fields
Abstract
We prove that if K is an infinite stable field whose generic type has weight 1 then K is separably closed. We also obtain partial results when the generic of K has finite weight and when K is strongly stable.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Algebraic Geometry and Number Theory · Mathematical Dynamics and Fractals