Sentence examples for finite types from inspiring English sources

Quantification over sets of such sets (or of n-tuples of such sets or over properties and relations of such sets) as are considered in second-order logic gives rise to third-order logic; and all logics of finite order form together the (simple) theory of (finite) types.

And this relation is not a relation in the hierarchy of finite types.

In particular, the relation of satisfaction for LCC is a relation that can be found in the hierarchy of finite types.

The problem is that in 1933 Tarski adopts as the mathematical apparatus of his metalanguages the simple theory of finite types, or equivalently, LGTC.

Suffice it to say that it is a version of a typical simple theory of finite types, with axioms and rules for the connectives and quantifiers, axioms of comprehension and extensionality for all orders, and an axiom of infinity.

An alternative to realizability semantics for intuitionistic arithmetic is Gödel's [1958] "Dialectica" interpretation, which associates with each formula B of L HA) a quantifier-free formula BD in the language of intuitionistic arithmetic of all finite types.

"There is a very finite type of building fitting our mold.

The GCM A is of finite type.

(2) The GCM A is of finite type.

(a) The GCM A is of finite type.

(3) Any sensitive subshift of finite type is cofinitely sensitive.