more from this thinker     |     more from this text

Single Idea 13661

[filed under theme 5. Theory of Logic / K. Features of Logics / 9. Expressibility ]

Full Idea

A logical language is 'semantically effective' if the collection of logically true sentences is a recursively enumerable set of strings.

Gist of Idea

A language is 'semantically effective' if its logical truths are recursively enumerable

Source

Stewart Shapiro (Foundations without Foundationalism [1991], 6.5)

Book Ref

Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.158

Related Idea

Idea 13660 Maybe compactness, semantic effectiveness, and the Löwenheim-Skolem properties are desirable [Shapiro]

The 2 ideas with the same theme [limits of what can be said in a logical language]:

10600 Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system [Smith,P]
13661 A language is 'semantically effective' if its logical truths are recursively enumerable [Shapiro]