There has been a great deal of recent interest in binarized neural networks, especially
because of their explainability. At the same time, automatic differentiation algorithms such as …

A structure M is pregeometric if the algebraic closure is a pregeometry in all structures
elementarily equivalent to M. We define a generalisation: structures with an existential …

This paper is devoted to o-minimalism, the study of the first-order properties of o-minimal
structures. The main protagonists are the pseudo-o-minimal structures, that is to say, the …

The differential field of transseries extends the field of real Laurent series and occurs in
various contexts: asymptotic expansions, analytic vector fields, and o-minimal structures, to …

If 𝐸⊆ ℝ𝑛 is closed and the structure (ℝ,+,⋅, 𝐸) is d-minimal (that is, in every structure
elementarily equivalent to (ℝ,+,⋅, 𝐸), every unary definable set is a disjoint union of open …

Let T be a consistent o-minimal theory extending the theory of densely ordered groups and
let T′ be a consistent theory. Then there is a complete theory T⁎ extending T such that T is …

AN ANALOGUE OF THE BAIRE CATEGORY THEOREM §1. Introduction. Let K be an expansion
of an ordered field (K, <, +, •). We say Page 1 THE JOURNAL OF SYMBOLIC LOGIC: Volume …

Let K be a subfield of the real field, D be a discrete subset of K and f: D^ n-> K be a function
such that f (D^ n) is somewhere dense. Then (K, f) defines the set of integers. We present …

Fix a language extending the language of ordered fields by at least one new predicate or
function symbol. Call an L-structure R pseudo-o-minimal if it is (elementarily equivalent to) …

Given a theory T of a polynomially bounded o-minimal expansion R of ̄ R= ⟨ R,+,., 0, 1,< ⟩
R¯=⟨ R,+,., 0, 1,<⟩ with field of exponents QQ, we introduce a theory TT whose models are …