Ample Hierarchy
Andreas Baudisch, Amador Martin-Pizarro, Martin Ziegler
TL;DR
This paper extends the concept of free pseudospace to higher dimensions, demonstrating its stability and ampleness properties, and provides a detailed analysis of forking and canonical bases in this context.
Contribution
It generalizes the free pseudospace construction to higher dimensions and characterizes its stability and ampleness properties in the framework of stable theories.
Findings
The n-dimensional free pseudospace is -stable and n-ample.
It is not (n+1)-ample, including not being 3-ample.
Provides an explicit description of canonical bases and forking.
Abstract
The ample hierarchy of geometries of stables theories is strict. We generalise the construction of the free pseudospace to higher dimensions and show that the n-dimensional free pseudospace is \omega-stable n-ample yet not (n+1)-ample. In particular, the free pseudospace is not 3-ample. A thorough study of forking is conducted and an explicit description of canonical bases is exhibited.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topology and Set Theory · Logic, programming, and type systems