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A viewpoint on amalgamation classes

Silvia Barbina, Domenico Zambella (2010)

Commentationes Mathematicae Universitatis Carolinae

We give a self-contained introduction to universal homogeneous models (also known as rich models) in a general context where the notion of morphism is taken as primitive. We produce an example of an amalgamation class where each connected component has a saturated rich model but the theory of the rich models is not model-complete.

Affine spaces as models for regular identities

Jung R. Cho, Józef Dudek (2002)

Colloquium Mathematicae

In [7] and [8], two sets of regular identities without finite proper models were introduced. In this paper we show that deleting one identity from any of these sets, we obtain a set of regular identities whose models include all affine spaces over GF(p) for prime numbers p ≥ 5. Moreover, we prove that this set characterizes affine spaces over GF(5) in the sense that each proper model of these regular identities has at least 13 ternary term functions and the number 13 is attained if and only if the...

Alcune osservazioni sul linguaggio L ( Q 1 )

Aroldo Goretti (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

An existence theorem for 1-atomic standard models of L ω ω ( Q 1 ) (more weak than usual “atomic models”) and applications of L ω ω ( Q 1 ) to L ω ω are the results of this note.

Algebraic approximation of analytic sets definable in an o-minimal structure

Marcin Bilski, Kamil Rusek (2010)

Annales Polonici Mathematici

Let K,R be an algebraically closed field (of characteristic zero) and a real closed field respectively with K=R(√(-1)). We show that every K-analytic set definable in an o-minimal expansion of R can be locally approximated by a sequence of K-Nash sets.

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