1. Michael H. Albert & Rami P. Grossberg (1990). Rich Models. Journal of Symbolic Logic 55 (3):1292-1298.
    We define a rich model to be one which contains a proper elementary substructure isomorphic to itself. Existence, nonstructure, and categoricity theorems for rich models are proved. A theory T which has fewer than $\min(2^\lambda,\beth_2)$ rich models of cardinality $\lambda(\lambda > |T|)$ is totally transcendental. We show that a countable theory with a unique rich model in some uncountable cardinal is categorical in ℵ 1 and also has a unique countable rich model. We also consider a stronger notion of richness, (...)
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  2. Michael H. Albert (1987). A Preservation Theorem for EC-Structures with Applications. Journal of Symbolic Logic 52 (3):779-785.
    We characterize the model companions of universal Horn classes generated by a two-element algebra (or ordered two-element algebra). We begin by proving that given two mutually model consistent classes M and N of L (respectively L') structures, with $\mathscr{L} \subseteq \mathscr{L}'$ , M ec = N ec ∣ L , provided that an L-definability condition for the function and relation symbols of L' holds. We use this, together with Post's characterization of ISP(A), where A is a two-element algebra, to show (...)
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  3. Michael H. Albert & Ross Willard (1987). Injectives in Finitely Generated Universal Horn Classes. Journal of Symbolic Logic 52 (3):786-792.
    Let K be a finite set of finite structures. We give a syntactic characterization of the property: every element of K is injective in ISP(K). We use this result to establish that A is injective in ISP(A) for every two-element algebra A.
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