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Some decidable theories with finitely many covers which are decidable and algorithmically found

Cornelia Kalfa (1994)

Colloquium Mathematicae

In any recursive algebraic language, I find an interval of the lattice of equational theories, every element of which has finitely many covers. With every finite set of equations of this language, an equational theory of this interval is associated, which is decidable with decidable covers that can be algorithmically found. If the language is finite, both this theory and its covers are finitely based. Also, for every finite language and for every natural number n, I construct a finitely based decidable...

Some model theory of SL(2,ℝ)

Jakub Gismatullin, Davide Penazzi, Anand Pillay (2015)

Fundamenta Mathematicae

We study the action of G = SL(2,ℝ), viewed as a group definable in the structure M = (ℝ,+,×), on its type space S G ( M ) . We identify a minimal closed G-flow I and an idempotent r ∈ I (with respect to the Ellis semigroup structure * on S G ( M ) ). We also show that the “Ellis group” (r*I,*) is nontrivial, in fact it is the group with two elements, yielding a negative answer to a question of Newelski.

Some (non-)elimination results for curves in geometric structures

Serge Randriambololona, Sergei Starchenko (2011)

Fundamenta Mathematicae

We show that the first order structure whose underlying universe is ℂ and whose basic relations are all algebraic subsets of ℂ² does not have quantifier elimination. Since an algebraic subset of ℂ² is either of dimension ≤ 1 or has a complement of dimension ≤ 1, one can restate the former result as a failure of quantifier elimination for planar complex algebraic curves. We then prove that removing the planarity hypothesis suffices to recover quantifier elimination: the structure with the universe...

Some results about compact logics

Paolo Lipparini (1982)

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

Nell'ambito della Teoria dei Modelli Astratta è possibile dimostrare che una logica compatta L è univocamente determinata dalla sua relazione di L-elementare equivalenza (Teorema 1). Si enunciano poi alcuni risultati sulle logiche massime correlate a certe relazioni di equivalenza e sulle logiche compatte generate da qualche sistema di Fraissé-Ehrenfeucht.

Special m-hyperidentities in biregular leftmost graph varieties of type (2,0)

Apinant Anantpinitwatna, Tiang Poomsa-ard (2009)

Discussiones Mathematicae - General Algebra and Applications

Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies a term equation s ≈ t if the corresponding graph algebra A ( G ) ̲ satisfies s ≈ t. A class of graph algebras V is called a graph variety if V = M o d g Σ where Σ is a subset of T(X) × T(X). A graph variety V ' = M o d g Σ ' is called a biregular leftmost graph variety if Σ’ is a set of biregular leftmost term equations. A term equation s ≈ t is called an identity in a variety...

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