A representation of models of Peano arithmetic
A representation theorem for Post-like algebras
A rigid Boolean algebra that admits the elimination of Q21
Using ♢ , we construct a rigid atomless Boolean algebra that has no uncountable antichain and that admits the elimination of the Malitz quantifier .
A saturation property on ideals
A scoop from groups: equational foundations for loops
Groups are usually axiomatized as algebras with an associative binary operation, a two-sided neutral element, and with two-sided inverses. We show in this note that the same simplicity of axioms can be achieved for some of the most important varieties of loops. In particular, we investigate loops of Bol-Moufang type in the underlying variety of magmas with two-sided inverses, and obtain ``group-like'' equational bases for Moufang, Bol and C-loops. We also discuss the case when the inverses are only...
A simple tree and its application to a counterexample of Philips.
A splitting theorem for ℱ-products
A sufficient condition for a variety to have the amalgamation property
A ternary variety generated by lattices
A theorem on generic intersections in an o-minimal structure
Consider a transitive definable action of a Lie group G on a definable manifold M. Given two (locally) definable subsets A and B of M, we prove that the dimension of the intersection σ(A) ∩ B is not greater than the expected one for a generic σ ∈ G.
A topological interpretation of second-order intuitionistic arithmetic
A type-open minimal model.
A unifying approach to theorems on preservation and interpolation for binary relations between structures.
A viewpoint on amalgamation classes
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.
A weakening of the axiom of choice for the standard binary tree.
A Word on the Joint Embedding Property
Abelian profinite groups
About the admissible predicates on admissible sets.
Absence of the interpolation property in the calculi and .
Absolutely saturated models