The expressiveness of the declarative language G odel can be improved by adding to it bounded quanti cations, i.e., quanti cations over nite domains, and arrays. Many problems can be expressed more concisely using bounded quanti cations than using recursion. Arrays are natural for many applications, e.g., in scienti c computing, and are conveniently used in bounded quanti cations. Treating bou...

Let $mathfrak{L}$ be the Virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. We investigate the structure of the Lie triplederivation algebra of $mathfrak{L}$ and $mathfrak{g}$. We provethat they are both isomorphic to $mathfrak{L}$, which provides twoexamples of invariance under triple derivation.

The moment map is a mathematical expression of the concept of the conservation associated with the symmetries of a Hamiltonian system. The abstract moment map is defined from G-manifold M to dual Lie algebra of G. We will interested study maps from G-manifold M to spaces that are more general than dual Lie algebra of G. These maps help us to reduce the dimension of a manifold much more.

We prove the equivalence of semantic version Tarski's theorem on undefinability truth with a Diagonal Lemma, and also show syntactic Undefinability Theorem weak diagonal lemma. outline two seemingly diagonal-free proofs for these theorems from literature, that can deliver G\"odel-Rosser's Incompleteness Theorem.

Computably enumerable (c.e.) reals can be coded by Chaitin machines through their halting probabilities. Tuning Solovay’s construction of a Chaitin universal machine for which ZFC (if arithmetically sound) cannot determine any single bit of the binary expansion of its halting probability, we show that every c.e. random real is the halting probability of a universal Chaitin machine for which ZFC...

let $mathfrak{l}$ be the virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. we investigate the structure of the lie triplederivation algebra of $mathfrak{l}$ and $mathfrak{g}$. we provethat they are both isomorphic to $mathfrak{l}$, which provides twoexamples of invariance under triple derivation.

We draw an analogy between Godel's Incompleteness Theorem in mathematics, and the impossibility of achieving a Universal Computer in computer science. Speci cally, Godel proved that there exist formal systems of mathematics that are consistent but not complete. In the same way, we show that there does not exist a general-purpose computer that is universal in the sense of being able to simulat...

In this paper, first we study the semi maximal filters in linear $BL$-algebras and we prove that any semi maximal filter is a primary filter. Then, we investigate the radical of semi maximal filters in $BL$-algebras. Moreover, we determine the relationship between this filters and other types of filters in $BL$-algebras and G"{o} del algebra. Specially, we prove that in a G"{o}del algebra, any ...

We study the propagation of Maxwellian electromagnetic waves in curved spacetimes terms appropriate geometrical optics limit, notions signal speed, and minimal coupling prescription from theory flat spacetime. In course this, we counter a recent major claim by Asenjo Hojman (2017) to effect that limit is partly ill-defined G\"odel spacetime; thereby dissolve present tension concerning establish...

We argue that only exact, comprehensive, and explicit solutions for the fundamental models, Klein-Gordon (KG) oscillators KG-Coulomb, would help to understand effects of gravitational fields on dynamics such quantum mechanical systems. In current methodical proposal, generated by a G\"odel-type Som-Raychaudhuri (SR) cosmic string spacetime KG-oscillators (KG-particles in general) are studied re...