We prove a downward transfer from categoricity in a successor in tame abstract elementary classes (AECs). This complements the upward transfer of Grossberg and VanDieren and improves the Hanf number in Shelah’s downward transfer (provided the class is tame). Theorem 0.1. Let K be an AEC with amalgamation. If K is LS(K)-weakly tame and categorical in a successor λ ≥ i(2LS(K))+ , then K is catego...

The condition number of the matrix of electro-acoustic headrelated transfer functions (HRTF) in a two-channel sound reproduction system has been used as a measure of robustness of the Atal-Schroeder crosstalk canceler. A comparative study has been made using results produced by computer simulations and HRTFs measured in an anechoic chamber by means of a dummy head. It has been found that acoust...

The status of the electro-excitation program to study baryon resonances at Jefferson Lab will be exemplified by the most recent results on resonance parameters and transition form factors in single and double-pion production. These results demonstrate that the separation of resonance and background contributions and therefore the extraction of the electro-coupling amplitudes of resonances becom...

We observe how a classical model-theoretic fact proves the existence of many strong amalgamation bases for the class ofR-embeddable von Neumann algebras, where R is the hyperfinite II1 factor. In particular, we shows that R itself is a strong amalgamation base.

Two-dimensional (2D) polyacrylic acid (PAA) nano-nets that comprise interlinked ultrathin nanowires with diameters of 10-30 nm are successfully prepared by a facile electro-netting process. Nano-nets feature a clear geometric characteristic with ideal and weighted Steiner networks due to the rapid phase separation process and its obeyed minimal energy principle. The versatile nano-nets create e...

Lead is a major cause of environmental concern for the industries like paint, pesticides, battery, mine, smelting etc. Lead can cause diseases related to kidney, liver, brain and nervous system. Various methods used for lead removal include electro-coagulation, ion exchange, membrane separation and suspended and attached growth biological techniques. In case of electro-coagulation, factors like...

This is a sequel to the paper [6] ‘Homology of types in model theory I: Basic concepts and connections with type amalgamation’. We compute the group H2 for strong types in stable theories and show that any profinite abelian group can occur as the group H2 in the model-theoretic context. The work described in this paper was originally inspired by Hrushovski’s discovery [8] of striking connection...

We describe the major result on categoricity in Lω1,ω , placing it in the context of more general work in abstract elementary classes. In particular, we illustrate the role of higher dimensional amalgamations and sketch the role of a weak extension of ZFC in the proof. We expound the translation of the problem to studying atomic models of first order theories. We provide a simple example of the...

We study when classes can have the disjoint amalgamation property for a proper initial segment of cardinals. Theorem A. For every natural number k, there is a class Kk defined by a sentence in Lω1,ω that has no models of cardinality greater than ik+1, but Kk has the disjoint amalgamation property on models of cardinality less than or equal to אk−3 and has models of cardinality אk−1. More strong...

Theorem. For each 2 ≤ k < ω there is an Lω1,ω-sentence φk such that: (1) φk is categorical in μ if μ ≤ אk−2; (2) φk is not אk−2-Galois stable; (3) φk is not categorical in any μ with μ > אk−2; (4) φk has the disjoint amalgamation property; (5) For k > 2, (a) φk is (א0,אk−3)-tame; indeed, syntactic first-order types determine Galois types over models of cardinality at most אk−3; (b) φk is אm-Gal...