Add to ORKGIn this very short paper, we bring together some very basic definitions and facts regarding the inductive definability of classes of finite structures. In particular, we give a necessary and sufficient condition on the expressibility of finiteness, the property that the domain of a structure is finite. There is an essential distinguishing feature between elementary and inductive sentences: the ability to express finiteness. First, some background. Definition: K is an elementary class of structures if there is a first-order sentence f such that
Abstract. A definition of finiteness is a set-theoretical property of a set that, if the Axiom of Ch...
The functions of finite support have played a ubiquitous role in the study of inductive inference si...
We prove that first order logic is strictly weaker than fixed point logic over every infinite classe...
In this dissertation, I investigate some questions about the model theory of finite structures. One ...
This paper proposes a notion of finitely-verifiable classes of sentences. Informally, a class of sen...
We develop a novel formal theory of finite structures, based on a view of finite structures as a fun...
We develop a novel formal theory of finite structures, based on a view of finite structures as a fun...
This book presents the main results of descriptive complexity theory, that is, the connections betwe...
Six definitions of a finite set are studied; and each implication between the definitions is shown t...
Finite-model theory is a study of the logical properties of finite mathematical structures. This pap...
Abstract: "We give a simple proof of a theorem of Gurevich and Shelah, that the inductive closure of...
Our research deals with several aspects of Definability and Computability on Finite Structures. Amon...
AbstractThe extensions of first-order logic with a least fixed point operator (FO + LFP) and with a ...
The functions of finite support have played a ubiquitous role in the study of inductive inference si...
The functions of finite support have played a ubiquitous role in the study of inductive inference si...
Abstract. A definition of finiteness is a set-theoretical property of a set that, if the Axiom of Ch...
The functions of finite support have played a ubiquitous role in the study of inductive inference si...
We prove that first order logic is strictly weaker than fixed point logic over every infinite classe...
In this dissertation, I investigate some questions about the model theory of finite structures. One ...
This paper proposes a notion of finitely-verifiable classes of sentences. Informally, a class of sen...
We develop a novel formal theory of finite structures, based on a view of finite structures as a fun...
We develop a novel formal theory of finite structures, based on a view of finite structures as a fun...
This book presents the main results of descriptive complexity theory, that is, the connections betwe...
Six definitions of a finite set are studied; and each implication between the definitions is shown t...
Finite-model theory is a study of the logical properties of finite mathematical structures. This pap...
Abstract: "We give a simple proof of a theorem of Gurevich and Shelah, that the inductive closure of...
Our research deals with several aspects of Definability and Computability on Finite Structures. Amon...
AbstractThe extensions of first-order logic with a least fixed point operator (FO + LFP) and with a ...
The functions of finite support have played a ubiquitous role in the study of inductive inference si...
The functions of finite support have played a ubiquitous role in the study of inductive inference si...
Abstract. A definition of finiteness is a set-theoretical property of a set that, if the Axiom of Ch...
The functions of finite support have played a ubiquitous role in the study of inductive inference si...
We prove that first order logic is strictly weaker than fixed point logic over every infinite classe...