On a universal axiomatization of the real closed fields
This paper presents a natural axiomatization of the real closed fields. It is universal and admits quantifier elimination.
On a variety of infinite algebras
On a weak Kelley-Morse theory of classes
On acyclic hypergraphs of minimal prime models.
On automorphisms of computability potential scales for -element algebras.
On axiomatizability and preservation in Kripke models.
On Borel reducibility in generalized Baire space
We study the Borel reducibility of Borel equivalence relations on the generalized Baire space for an uncountable κ with . The theory looks quite different from its classical counterpart where κ = ω, although some basic theorems do generalize.
On cardinalities of algebras of formulas for -categorical theories
On clones determined by their initial segments
On compact classes of models
On constructive nilpotent groups.
On constructivizability of the tensor product of modules.
On convergence of integrals in o-minimal structures on archimedean real closed fields
We define a notion of volume for sets definable in an o-minimal structure on an archimedean real closed field. We show that given a parametric family of continuous functions on the positive cone of an archimedean real closed field definable in an o-minimal structure, the set of parameters where the integral of the function converges is definable in the same structure.
On countably compact reduced products, III
On countably universal Boolean algebras compact classes of models
On definably proper maps
In this paper we work in o-minimal structures with definable Skolem functions, and show that: (i) a Hausdorff definably compact definable space is definably normal; (ii) a continuous definable map between Hausdorff locally definably compact definable spaces is definably proper if and only if it is a proper morphism in the category of definable spaces. We give several other characterizations of definably proper, including one involving the existence of limits of definable types. We also prove the...
On d-finite tuples in random variable structures
We prove that the d-finite tuples in models of ARV are precisely the discrete random variables. Then, we apply d-finite tuples to the work by Keisler, Hoover, Fajardo, and Sun concerning saturated probability spaces. In particular, we strengthen a result in Keisler and Sun's recent paper.
On d-finiteness in continuous structures
We observe that certain classical results of first order model theory fail in the context of continuous first order logic. We argue that this happens since finite tuples in a continuous structure may behave as infinite tuples in classical model theory. The notion of a d-finite tuple attempts to capture some aspects of the classical finite tuple behaviour. We show that many classical results involving finite tuples are valid in continuous logic upon replacing "finite" with "d-finite". Other results,...
On divisibility in definable groups
Let ℳ be an o-minimal expansion of a real closed field. It is known that a definably connected abelian group is divisible. We show that a definably compact definably connected group is divisible.
On effective presentations of formal concept lattices.