LF groups, aec amalgamation, few automorphisms

2019/01/28 by Saharon Shelah, Shelah, Saharon
Mathematics · Computer Science · #Advanced Topology and Set Theory #Homotopy and Cohomology in Algebraic Topology #Computability, Logic, AI Algorithms

paper · pdf · doi:10.48550/arxiv.1901.09747

Abstract

In S. 1 we deal with amalgamation bases, e.g., we define when an a.e.c. k has (λ,κ)-amalgamation which means "many" M in K^k_λ are amalgamation bases. We then consider what happens for the class of lf groups. In S. 2 we deal with weak definability of a ∈ N∖ M over M, for K_exlf. In S. 3 we deal with indecomposable members of K_exlf and with the existence of universal members of K^k_μ, for μ strong limit of cofinality ℵ₀. Most noteworthy: if K_lf has a universal model in μ then it has a canonical one similar to the special models, (the parallel to saturated ones in this cardinality). In S. 4 we prove "every G ∈ K^lf_

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