# How can certain predicates be proven to not have sets as their extension?

## What is the extension of a predicate?

The “extension” of a predicate (relative to an interpretation) is simply the collection of all things to which it truly applies. If the universe of discourse happens to be finite, and indeed rather small, the extension of predicates can be given by means of a table.

## Is a predicate a set?

In set theory with excluded middle, predicates are understood to be characteristic functions or set indicator functions (i.e., functions from a set element to a truth value). Set-builder notation makes use of predicates to define sets.

## Is an extension to propositional logic?

It should be viewed as an extension to propositional logic, in which the notions of truth values, logical connectives, etc still apply but propositional letters(which used to be atomic elements), will be replaced by a newer notion of proposition involving predicates and quantifiers.

## What is an extension logic?

extension, in logic, correlative words that indicate the reference of a term or concept: “intension” indicates the internal content of a term or concept that constitutes its formal definition; and “extension” indicates its range of applicability by naming the particular objects that it denotes.

## What is the extension of a set?

The extension of an object in abstract algebra, such as a group, is the underlying set of the object. The extension of a set is the set itself. That a set can capture the notion of the extension of anything is the idea behind the axiom of extensionality in axiomatic set theory.

## What is an example of extension?

The definition of an extension is an addition such as to a building, an extra phone line connected to the main line or an extra amount of time given to someone to pay a debt. An example of an extension is adding a second story to a single story house.

## Can a term have an extension but no intension?

Some terms have an intension, but no extension: they have an empty extension.

## What is the difference between intention and extension?

intension and extension, in logic, correlative words that indicate the reference of a term or concept: “intension” indicates the internal content of a term or concept that constitutes its formal definition; and “extension” indicates its range of applicability by naming the particular objects that it denotes.

## What are the differences between extension and intension in meaning?

Intension refers to the logical or definitional conditions that specify the set of all possible things a word or phrase could describe, while extension refers to the set of all actual things the word or phrase describes.

## What is meant by meaning extension in semantic?

The extension of semantic meaning refers to extend a word’s meaning according to the context and logical relations and select an exact word in the target language, so as to make the translation more natural, native and smooth.

## What is an example of logical extension?

We welcome feedback: you can select the flag against a sentence to report it. A merger between the titles would be a logical extension of those discussions. Some see this job as a logical extension of that belief. Extending this idea to a global level, where the opportunitiesare greater, isa logical extension.

## Is denotation the same as extension?

The denotation of a word or a phrase is the set of things in the world that the word refers to. So one denotation for the word pencil is this pencil right here. All of these things are denotations for the word pencil. Another word for denotation is extension.