Notes on a Strengthening of the Herwig–lascar Extension Theorem

ar X iv : 1 70 5 . 01 88 8 v 2 [ m at h . L O ] 1 8 Ju l 2 01 7 COHERENT EXTENSION OF PARTIAL AUTOMORPHISMS , FREE AMALGAMATION , AND AUTOMORPHISM GROUPS

We give strengthened versions of the Herwig–Lascar and Hodkinson–Otto extension theorems for partial automorphisms of finite structures. Such strengthenings yield several combinatorial and group-theoretic consequences for homogeneous structures. For instance, we establish a coherent form of the extension property for partial automorphisms for certain Fräıssé classes. We deduce from these result...

Extending Partial Automorphisms and the Proonite Topology on Free Groups

A class of structures C is said to have the extension property for partial automorphisms (EPPA) if, whenever C 1 and C 2 are structures in C, C 1 nite, C 1 C 2 , and p 1 , p 2 , : : :, p n are partial automorphisms of C 1 extending to automorphisms of C 2 , then there exist a nite structure C 3 in C and automorphisms 1 , 2 , : : :, n of C 3 extending the p i. We will prove that some classes of ...

Extending Partial Automorphisms and the Profinite Topology on Free Groups

A class of structures C is said to have the extension property for partial automorphisms (EPPA) if, whenever C1 and C2 are structures in C, C1 finite, C1 ⊆ C2, and p1, p2, . . . , pn are partial automorphisms of C1 extending to automorphisms of C2, then there exist a finite structure C3 in C and automorphisms α1, α2, . . . , αn of C3 extending the pi. We will prove that some classes of structur...

Finite conformal hypergraph covers and Gaifman cliques in finite structures

We provide a canonical construction of conformal covers for finite hypergraphs and present two immediate applications to the finite model theory of relational structures. In the setting of relational structures, conformal covers serve to construct guarded bisimilar companion structures that avoid all incidental Gaifman cliques – thus serving as a partial analogue in finite model theory for the ...

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials