Single Idea 13658

[catalogued under 5. Theory of Logic / J. Model Theory in Logic / 3. L÷wenheim-Skolem Theorems]

Full Idea

A language has the Downward L÷wenheim-Skolem property if each satisfiable countable set of sentences has a model whose domain is at most countable.

Gist of Idea

Downward L÷wenheim-Skolem: each satisfiable countable set always has countable models


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

Book Reference

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

A Reaction

This means you can't employ an infinite model to represent a fact about a countable set.

Related Idea

Idea 13659 Upward L÷wenheim-Skolem: each infinite model has infinite models of all sizes [Shapiro]