منابع مشابه
Finite Circular Definitions –
A finite circular definition is a particularly simple kind of circular definition. The content of a circular definition is given by a revision process that the definition generates. Finite circular definitions are those that have finite revision processes: the process of revision is complete, in the sense made precise below, in finitely many stages. Finite circular definitions prove to be usefu...
متن کاملTruth definitions in finite models
The paper discusses the notion of finite model truth definitions (or FM–truth definitions), introduced by M. Mostowski as a finite model analogue of Tarski’s classical notion of truth definition. We compare FM–truth definitions with Vardi’s concept of the combined complexity of logics, noting an important difference: the difficulty of defining FM–truth for a logic L does not depend on the synta...
متن کاملInductive Definitions Over Finite Structures
We give a simple proof of a theorem of Gurevich and Shelah, that the inductive closure of an inflationary operator is equivalent, over the class of finite structures, to the inductive closure (i.e. minimal fixpoint) of a positive operator. A variant of the same proof establishes a theorem of Immerman, that the class of inductive closures of positive first order operators is closed under complem...
متن کاملThe finite stages of inductive definitions
In general, the least fixed point of a positive elementary inductive definition over the Herbrand universe is Π 1 and has no computational meaning. The finite stages, however, are computable, since validity of equality formulas in the Herbrand universe is decidable. We set up a formal system BID for the finite stages of positive elementary inductive definitions over the Herbrand universe and sh...
متن کاملA finite axiomatisation of inductive-inductive definitions
Induction-induction is a principle for mutually defining data types A ∶ Set and B ∶ A→ Set. Both A and B are defined inductively, and the constructors for A can refer to B and vice versa. In addition, the constructor for B can refer to the constructor for A. Induction-induction occurs in a natural way when formalising dependent type theory in type theory. We give some examples of inductive-indu...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1989
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-133-3-169-177