25 citations · 76 across the 24 of their papers we have counts for
18 papers · 1 filter
Physics over a finite field and Wick rotation
Boris Zilber
The paper develops an earlier proposition that the physical universe is a finite system co-ordinatised by a very large finite field which looks like the f…
A topological -invariant
Boris Zilber
We suggest to look at formal sentences describing complex algebraic varieties together with their universal covers as topological invariants. We prove that for abelian varieties an…
On the Theory of Specialisations of Regular Covers of Zariski Structures
Ugur Efem, Boris Zilber
In algebraic geometry specialisations and valuations play and important role. In this paper we start investigating analogous structures for Zariski structures. Specifically, we loo…
Non-elementary categoricity and projective locally o-minimal classes
Boris Zilber
Given a cover of a family of smooth complex algebraic varieties, we associate with it a class containing , of structures locally definable i…
Modular curves and their pseudo-analytic cover
Boris Zilber, Chris Daw
We find a natural -axiomatisation of a structure on the upper half-plane as the covering space of modular curves. The main theorem states that has a…
A model theory section conjecture
Romin Abdolahzadi, Boris Zilber
We introduce the category of structures and interpretations which allows us to discuss some issues of Grothendieck's anabelian geometry in model-theory terms. Our main result is a…
Definability, interpretations and étale fundamental groups
Romin Abdolahzadi, Boris Zilber
The aim of the paper and of a wider project is to translate main notions of anabelian geometry into the language of model theory. Here we finish with giving the definition of the é…
Around logical perfection
John Alexander Cruz Morales, Andrés Villaveces, Boris Zilber
In this article we present and describe a notion of "logical perfection". We extract the notion of "perfection" from the contemporary logical concept of categoricity. Categoricity…
A model theoretic Rieffel's theorem of quantum 2-torus
Masanori Itai, Boris Zilber
We defined a notion of quantum 2-torus in "Masanori Itai and Boris Zilber, Notes on a model theory of quantum 2-torus for generic , arXiv:1503.06045v1 [mathLO]" an…
Analytic Zariski structures and non-elementary categoricity
Boris Zilber
We study analytic Zariski structures from the point of view of non-elementary model theory. We show how to associate an abstract elementary class with a one-dimensional analytic Za…
A non-desarguesian projective plane
Katrin Tent, Boris Zilber
We construct a new non-desarguesian projective plane from a complex analytic structure. At the same time the construction can be explained in terms of so called Hrushovski's constr…
Notes on a model theory of quantum 2-torus for generic q
Masanori Itai, Boris Zilber
We describe a structure over the complex numbers associated with the non-commutative algebra Aq called quantum 2-tori. These turn out to have uncountably categorical L_omega1,omega…
The theory of exponential sums
Boris Zilber
We consider the theory of algebraically closed fields of characteristic zero with multivalued operations (raising to powers). It is in fact the theory of equations i…
Natural models of theories of green points
Juan Diego Caycedo, Boris Zilber
We explicitly present expansions of the complex field which are models of the theories of green points in the multiplicative group case and in the case of an elliptic curve without…
Exponentially Closed Fields and the Conjecture on Intersections with Tori
Jonathan Kirby, Boris Zilber
We give an axiomatization of the class ECF of exponentially closed fields, which includes the pseudo-exponential fields previously introduced by the second author, and show that it…
Quantum Harmonic Oscillator as a Zariski Geometry
Vinesh Solanki, Dmitry Sustretov, Boris Zilber
We carry out a model-theoretic analysis of the Heisenberg algebra. To this end, a geometric structure is associated to the Heisenberg algebra and is shown to be a Zariski geometry.…
Covers of Multiplicative Groups of Algebraically Closed Fields of Arbitrary Characteristic
Martin Bays, Boris Zilber
We show that algebraic analogues of universal group covers, surjective group homomorphisms from a -vector space to with "standard kernel", are determined u…
Fields with pseudo-exponentiation
Boris Zilber
We study the structure of an algebraically closed field with extra function resembling the classical exponentiation on complex numbers.