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The weak extension property and finite axiomatizability for quasivarieties

Wiesław Dziobiak, Miklós Maróti, Ralph McKenzie, Anvar Nurakunov (2009)

Fundamenta Mathematicae

We define and compare a selection of congruence properties of quasivarieties, including the relative congruence meet semi-distributivity, RSD(∧), and the weak extension property, WEP. We prove that if 𝒦 ⊆ ℒ ⊆ ℒ' are quasivarieties of finite signature, and ℒ' is finitely generated while 𝒦 ⊨ WEP, then 𝒦 is finitely axiomatizable relative to ℒ. We prove for any quasivariety 𝒦 that 𝒦 ⊨ RSD(∧) iff 𝒦 has pseudo-complemented congruence lattices and 𝒦 ⊨ WEP. Applying these results and other results...

Théories de Galois différentielles et transcendance

Daniel Bertrand (2009)

Annales de l’institut Fourier

On décrit des preuves galoisiennes des versions logarithmique et exponentielle de la conjecture de Schanuel, pour les variétés abéliennes sur un corps de fonctions.

Thickness, and a categoric view of type-space functors

Itay Ben-Yaacov (2003)

Fundamenta Mathematicae

We define the class of thick cats (compact abstract theories, which contains in particular semi-Hausdorff, Hausdorff and first order cats), and prove that in this class simplicity behaves as in first order theories. We consider well-known first order notions, such as interpretability or stable dividing/reduct, and propose analogous notions that can be naturally expressed in terms of maps between type-space functors. We prove several desirable properties of the new notions and show the connection...

Topological dynamics of unordered Ramsey structures

Moritz Müller, András Pongrácz (2015)

Fundamenta Mathematicae

We investigate the connections between Ramsey properties of Fraïssé classes and the universal minimal flow M ( G ) of the automorphism group G of their Fraïssé limits. As an extension of a result of Kechris, Pestov and Todorcevic (2005) we show that if the class has finite Ramsey degree for embeddings, then this degree equals the size of M ( G ) . We give a partial answer to a question of Angel, Kechris and Lyons (2014) showing that if is a relational Ramsey class and G is amenable, then M ( G ) admits a unique invariant...

Triangulation in o-minimal fields with standard part map

Lou van den Dries, Jana Maříková (2010)

Fundamenta Mathematicae

In answering questions of J. Maříková [Fund. Math. 209 (2010)] we prove a triangulation result that is of independent interest. In more detail, let R be an o-minimal field with a proper convex subring V, and let st: V → k be the corresponding standard part map. Under a mild assumption on (R,V) we show that a definable set X ⊆ Vⁿ admits a triangulation that induces a triangulation of its standard part st X ⊆ kⁿ.

T-Varieties and Clones of T-terms

Klaus Denecke, Prakit Jampachon (2005)

Discussiones Mathematicae - General Algebra and Applications

The aim of this paper is to describe how varieties of algebras of type τ can be classified by using the form of the terms which build the (defining) identities of the variety. There are several possibilities to do so. In [3], [19], [15] normal identities were considered, i.e. identities which have the form x ≈ x or s ≈ t, where s and t contain at least one operation symbol. This was generalized in [14] to k-normal identities and in [4] to P-compatible identities. More generally, we select a subset...

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