Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Induction Models on $\mathbb{N}$
View through CrossRef
Mathematical induction is a fundamental tool in computer science and mathematics. Henkin [12] initiated the study of formalization of mathematical induction restricted to the setting when the base case B is set to singleton set containing 0 and a unary generating function S. The usage of mathematical induction often involves wider set of base cases and k−ary generating functions with different structural restrictions. While subsequent studies have shown several Induction Models to be equivalent, there does not exist precise logical characterization of reduction and equivalence among different Induction Models. In this paper, we generalize the definition of Induction Model and demonstrate existence and construction of S for given B and vice versa. We then provide a formal characterization of the reduction among different Induction Models that can allow proofs in one Induction Models to be expressed as proofs in another Induction Models. The notion of reduction allows us to capture equivalence among Induction Models.
Title: Induction Models on $\mathbb{N}$
Description:
Mathematical induction is a fundamental tool in computer science and mathematics.
Henkin [12] initiated the study of formalization of mathematical induction restricted to the setting when the base case B is set to singleton set containing 0 and a unary generating function S.
The usage of mathematical induction often involves wider set of base cases and k−ary generating functions with different structural restrictions.
While subsequent studies have shown several Induction Models to be equivalent, there does not exist precise logical characterization of reduction and equivalence among different Induction Models.
In this paper, we generalize the definition of Induction Model and demonstrate existence and construction of S for given B and vice versa.
We then provide a formal characterization of the reduction among different Induction Models that can allow proofs in one Induction Models to be expressed as proofs in another Induction Models.
The notion of reduction allows us to capture equivalence among Induction Models.
Related Results
DISCOVERY ON BEAL CONJECTURE
DISCOVERY ON BEAL CONJECTURE
In this paper we give a proof for Beal's conjecture . Since the discovery of the proof of Fermat's last theorem by Andre Wiles, several questions arise on the correctness of Be...
The Dynamical Mordell–Lang Conjecture for Skew-Linear Self-Maps. Appendix by Michael Wibmer
The Dynamical Mordell–Lang Conjecture for Skew-Linear Self-Maps. Appendix by Michael Wibmer
AbstractLet $k$ be an algebraically closed field of characteristic $0$, let $N\in{\mathbb{N}}$, let $g:{\mathbb{P}}^1{\longrightarrow } {\mathbb{P}}^1$ be a nonconstant morphism, a...
Multiple interpolation problem for functions with zero spherical mean
Multiple interpolation problem for functions with zero spherical mean
Let $|\cdot|$ be the Euclidean norm in $\mathbb{R}^n$, $n\geq 2$. For $r>0$, weLet $|\cdot|$ be the Euclidean norm in $\mathbb{R}^n$, $n\geq 2$. For $r>0$, we denote by $V_r(...
The Cayley Isomorphism Property for Cayley Maps
The Cayley Isomorphism Property for Cayley Maps
The Cayley Isomorphism property for combinatorial objects was introduced by L. Babai in 1977. Since then it has been intensively studied for binary relational structures: graphs, d...
INTEGRAL REPRESENTATION OF HYPERBOLICALLY CONVEX FUNCTIONS
INTEGRAL REPRESENTATION OF HYPERBOLICALLY CONVEX FUNCTIONS
An article consists of two parts.
In the first part the sufficient and necessary conditions for an integral representation of hyperbolically convex (h.c.) functions $k(x)$ $\left(...
Characterization of subfields of adelic algebras by a product formula
Characterization of subfields of adelic algebras by a product formula
Abstract
We consider projective, irreducible, non-singular curves over an algebraically closed field
$$\Bbbk $$
...
An Algebraic Approach to the Goldbach and Polignac Conjectures
An Algebraic Approach to the Goldbach and Polignac Conjectures
This paper will give both the necessary and sufficient conditions required to find a counter-example to the Goldbach Conjecture by using an algebraic approach where no knowledge of...
NONEXISTENCE RESULT FOR QUASILINEAR ELLIPTIC INEQUALITIES INVOLVING THE GRUSHIN OPERATOR
NONEXISTENCE RESULT FOR QUASILINEAR ELLIPTIC INEQUALITIES INVOLVING THE GRUSHIN OPERATOR
In this paper, we establish a nonexistence result of positive solutions of the inequality \( -{\rm div}_G \left( |\nabla_G u|^{p-2} \nabla_G u \right) \geq u^q \quad {\rm in} \; \m...