# Extension (semantics): Quiz

Question 1: That a set can capture the notion of the extension of anything is the idea behind the axiom of extensionality in ________.
Mathematical logicGeorg CantorSet theoryModel theory

Question 2: Some fundamental formulations in the field of ________ rely heavily on a valuation of extension over intension.
AristotleGeneral semanticsBertrand RussellLinguistic relativity

Question 3: The extension of an object in ________, such as a group, is the underlying set of the object.
Abstract algebraVector spaceNumber theoryAlgebraic structure

Question 4: In ________, some database textbooks use the term 'intension' to refer to the schema of a database, and 'extension' to refer to particular instances of a database.

Question 5: (Maybe they exist in other universes, and these universes are other "________"--possible alternatives to the actual world.) Perhaps some actual things are nonexistent.
AristotleModal logicSaul KripkePossible world

Question 6: This kind of extension is used so constantly in contemporary mathematics based on ________ that it can be called an implicit assumption.
Set theoryModel theoryGeorg CantorMathematical logic

Question 7: (Sherlock Holmes seems to be an 'actual' example of a fictional character; one might think there are many other characters ________ 'might' have invented, though he actually invented Holmes.)
Spiritualism (beliefs)SpiritualismHelen DuncanArthur Conan Doyle

Question 8: The extension of a whole statement, as opposed to a word or phrase, is defined (since ________ 1892) as its truth value.
Rudolf CarnapGottlob FregeBertrand RussellLogical positivism

Question 9: For example, the extension of a function is a set of ________ that pair up the arguments and values of the function; in other words, the function's graph.
Set (mathematics)Type theorySet theoryOrdered pair

Question 10: In ________, the 'extension' of a mathematical concept is the set that is specified by that concept.
Set theoryMathematicsGeometryMathematical logic