2 citations · 3 across the 8 of their papers we have counts for
11 papers
O-minimal open core is not an elementary property
Alexi Block Gorman, Esther Elbaz Saban
Given a structure with a definable topology, its open core is a structure defined on the same universe whose language consists of all open sets of all arities definab…
Sequential densities of rational languages
Alexi Block Gorman, Dominique Perrin
We introduce the notion of density of a rational language with respect to a sequence of probability measures. We prove that if is a sequence of Bernoulli measures convergin…
One-sided Hom shifts
Marie-Pierre Béal, Alexi Block Gorman
We prove that it is decidable whether a one-sided shift of finite type is conjugate to a one-sided Hom-shift, and whether a tree-shift of finite type is conjugate to a Hom tree-shi…
A Dichotomy for -automatic expansions of Presburger Arithmetic
Jason Bell, Alexi Block Gorman, Chris Schulz
Let and let be a subset of the natural numbers that is -automatic and not eventually periodic. We show that the following dichotomy holds: either all -automatic…
Sparse regular subsets of the reals
Jason Bell, Alexi Block Gorman
This paper concerns the expansion of the real ordered additive group by a predicate for a subset of whose base- representations are recognized by a Büchi automaton. In t…
Pathological examples of structures with o-minimal open core
Alexi Block Gorman, Erin Caulfield, Philipp Hieronymi
This paper answers several open questions around structures with o-minimal open core. We construct an expansion of an o-minimal structure by a unary predicate such th…
Companionability Characterization for the Expansion of an O-minimal Theory by a Dense Subgroup
Alexi Block Gorman
This paper provides a full characterization for when the expansion of a complete o-minimal theory by a unary predicate that picks out a divisible dense and codense subgroup has a m…
Continuous Regular Functions
Alexi Block Gorman, Philipp Hieronymi, Elliot Kaplan +5
Following Chaudhuri, Sankaranarayanan, and Vardi, we say that a function is -regular if there is a Büchi automaton that accepts precisely the set of base $r…
Pairs of Theories Satisfying a Mordell-Lang Condition
Alexi Block Gorman, Philipp Hieronymi, Elliot Kaplan
This paper proposes a new setup for studying pairs of structures. This new framework includes many of the previously studied classes of pairs, such as dense pairs of o-minimal stru…
Nil-good and nil-good clean matrix rings
Alexi Block Gorman, Wing Yan Shiao
The notion of clean rings and 2-good rings have many variations, and have been widely studied. We provide a few results about two new variations of these concepts and discuss the t…
The density of primes dividing a particular non-linear recurrence sequence
Alexi Block Gorman, Tyler Genao, Heesu Hwang +3
Define the sequence by , and $$b_n=\begin{cases} \frac{b_{n-1}b_{n-3}-b_{n-2}^2}{b_{n-4}}&\textrm{if}~ n\not\equiv 0\pmod 3, \frac{b_{n-1}b_{n-3…