Related papers: Prenex normal form theorems in semi-classical arit…
A new totally algebraic formalism based on general, abstract ladder operators has been proposed. This approach heavily grounds in the superoperator formalism of Primas. However it is necessary to introduce many improvements in his…
Regular and higher regular graded algebras (in simplest case satisfying Von Neumann regularity $\Theta_{1}\Theta_{2}\Theta_{1}=\Theta_{1}$ instead of anticommutativity) are introduced and their properties are studied. They are described in…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
This note documents the specification of normal forms in cubical type theory. The definition is already present in the proof of normalization for cubical type theory, but we present it in a more traditional style explicitly for reference.
Non-archimedean fields with restricted analytic functions may not support a full exponential function, but they always have partial exponentials defined in convex subrings. On face of this, we study the first order theory of the class of…
The (.)_reg construction was introduced in order to make an arbitrary semigroup S divide a regular semigroup (S)_reg which shares some important properties with S (e.g., finiteness, subgroups, torsion bounds, J-order structure). We show…
Going back to Kreisel in the Sixties, hyperarithmetical analysis is a cluster of logical systems just beyond arithmetical comprehension. Only recently natural examples of theorems from the mathematical mainstream were identified that fit…
In the present paper we construct normal numbers in base $q$ by concatenating $q$-ary expansions of pseudo polynomials evaluated at the primes. This extends a recent result by Tichy and the author.
Normal forms for logic programs under stable/answer set semantics are introduced. We argue that these forms can simplify the study of program properties, mainly consistency. The first normal form, called the {\em kernel} of the program, is…
In the present paper the authors construct normal numbers in base $q$ by concatenating $q$-adic expansions of prime powers $\lfloor\alpha p^\theta\rfloor$ with $\alpha>0$ and $\theta>1$.
We establish results with an arithmetic flavor that generalize the polynomial multidimensional Szemeredi theorem and related multiple recurrence and convergence results in ergodic theory. For instance, we show that in all these statements…
This paper develops the basic theory of formal schemes over fields in the supersymmetric setting. We introduce the notion of a formal superscheme and investigate some of its fundamental properties. Particular emphasis is placed on the study…
Given a first-order sentence, a model-checking computation tests whether the sentence holds true in a given finite structure. Data provenance extracts from this computation an abstraction of the manner in which its result depends on the…
We present a detailed proof of the prime number theorem suitable for a typical undergraduate- or graduate-level complex analysis course. Our presentation is particularly useful for any instructor who seeks to use the prime number theorem…
Consensus is a well-studied problem in distributed sensing, computation and control, yet deriving useful and easily computable bounds on the rate of convergence to consensus remains a challenge. This paper discusses the use of seminorms for…
It is well known that pretameness implies the forcing theorem, and that pretameness is characterized by the preservation of the axioms of $\mathsf{ZF}^-$, that is $\mathsf{ZF}$ without the power set axiom, or equivalently, by the…
Let M be a polynomially bounded, o-minimal structure with archimedean prime model, for example if M is a real closed field. Let C be a convex and unbounded subset of M. We determine the first order theory of the structure M expanded by the…
The method of Tur\'an in establishing the normal order for the number of prime divisors of a number is used to show that a certain class of arithmetic functions do not have a normal order.
We show that the first order theory of the lattice of open sets in some natural topological spaces is $m$-equivalent to second order arithmetic. We also show that for many natural computable metric spaces and computable domains the first…
Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring over a field and $A$ a standard graded $S$-algebra. In terms of the Gr\"obner basis of the defining ideal $J$ of $A$ we give a condition, called the x-condition, which implies that all graded…