Related papers: Some results on $\mathbb{R}$-computable structures
The ordered structures of natural, integer, rational and real numbers are studied here. It is known that the theories of these numbers in the language of order are decidable and finitely axiomatizable. Also, their theories in the language…
We construct a fully faithful functor from the category of graphs to the category of fields. Using this functor, we resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure S,…
The literature for count modeling provides useful tools to conduct causal inference when outcomes take non-negative integer values. Applied to the potential outcomes framework, we link the Bayesian causal inference literature to statistical…
The ordered structures of natural, integer, rational and real numbers are studied in this thesis. The theories of these numbers in the language of order are decidable and finitely axiomatizable. Also, their theories in the language of order…
Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable representative in their topological conjugacy class. Most natural…
A mathematical model, describing some different weaving structures, is made in this article. The terms self-mirror and rotation-stable weaving structure are initiated here. There are used the properties and operations in the set of the…
This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple…
Cantor's ordinal numbers, a powerful extension of the natural numbers, are a cornerstone of set theory. They can be used to reason about the termination of processes, prove the consistency of logical systems, and justify some of the core…
We analyze the effective content of countable, second countable topological spaces by directly calculating the complexity of several topologically defined index sets. We focus on the separation principles, calibrating an arithmetic…
We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…
We look more carefully at the modeling of causality using structural equations. It is clear that the structural equations can have a major impact on the conclusions we draw about causality. In particular, the choice of variables and their…
Computational models pervade all branches of the exact sciences and have in recent times also started to prove to be of immense utility in some of the traditionally 'soft' sciences like ecology, sociology and politics. This volume is a…
We investigate different notions of "computable topological base" for represented spaces. We show that several non-equivalent notions of bases become equivalent when we consider computably enumerable bases. This indicates the existence of a…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
We briefly review the strategy to perform non-perturbative heavy quark effective theory computations and we specialize to the case of the b quark mass which has recently been computed including the 1/m term.
We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…
Recent results show that a constraint satisfaction problem (CSP) defined over rational numbers with their natural ordering has a solution if and only if it has a definable solution. The proof uses advanced results from topology and modern…
We present a method for constructing countable models of small theories and apply it to prove theorems on the maximal number of countable non-isomorphic models of linearly ordered theories.
The class of abelian $p$-groups are an example of some very interesting phenomena in computable structure theory. We will give an elementary first-order theory $T_p$ whose models are each bi-interpretable with the disjoint union of an…
Manifold learning and effective model building are generally viewed as fundamentally different types of procedure. After all, in one we build a simplified model of the data, in the other, we construct a simplified model of the another…