Related papers: Primitive Recursive Ordered Fields and Some Applic…
We prove that the Lie algebra of primitive elements of a graded and connected bialgebra, free as an associative algebra, over a eld of characteristic zero, is a free Lie algebra. The main tool is a ltration, which allows to embed the…
We initiate the study of computable presentations of real and complex C*-algebras under the program of effective metric structure theory. With the group situation as a model, we develop corresponding notions of recursive presentations and…
S-Motzkin paths (bijective to ternary trees) and partial version of them are calculated using only elementary methods from linear algebra.
We study versions of the tree pigeonhole principle, $\mathsf{TT}^1$, in the context of Weihrauch-style computable analysis. The principle has previously been the subject of extensive research in reverse mathematics. Two outstanding…
We prove a recursive identity involving formal iterated logarithms and formal iterated exponentials. These iterated logarithms and exponentials appear in a natural extension of the logarithmic formal calculus used in the study of…
The two main approaches to the study of irreducible representations of orders (via traces and Poisson orders) have so far been applied in a completely independent fashion. We define and study a natural compatibility relation between the two…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
Combinatorial objects such as rooted trees that carry a recursive structure have found important applications recently in both mathematics and physics. We put such structures in an algebraic framework of operated semigroups. This framework…
We introduce ordinal collapsing principles that are inspired by proof theory but have a set theoretic flavor. These principles are shown to be equivalent to iterated $\Pi^1_1$-comprehension and the existence of admissible sets, over weak…
We show that the common theory of all modules over a tubular algebra (over a recursive algebraically closed field) is decidable. This result supports a long standing conjecture of Mike Prest which says that a finite-dimensional algebra…
This paper is a continuation of our previous works where we study maps from $X_0(N)$, $N \ge 1$, into $\mathbb P^2$ constructed via modular forms of the same weight and criteria that such a map is birational (see [12]). In the present paper…
In this paper, we show that VC-minimal ordered fields are real closed. We introduce a notion, strictly between convexly orderable and dp-minimal, that we call dp-small, and show that this is enough to characterize many algebraic theories.…
If local forms of Littlewood's three principles are stated as axioms for an ordered field, then each principle is equivalent to the completeness axiom.
We prove that a sequence is primitive substitutive if and only if the set of its derived sequences is finite; we defined these sequences here.
Common meadows are commutative and associative algebraic structures with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. The inverse of zero is an error term…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
Query evaluation in monadic second-order logic (MSO) is tractable on trees and treelike instances, even though it is hard for arbitrary instances. This tractability result has been extended to several tasks related to query evaluation, such…
Two approaches are developed to exploit, for simple complex or compact real Lie algebras g, the information that stems from the characteristic equations of representation matrices and Casimir operators. These approaches are selected so as…
We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…