Sentence examples for formalized theories from inspiring English sources

PRA, or something equivalent to it, is sufficient for developing the theory of syntax for formalized theories.

Notions that climate plays a major dynamic role in landform evolution were in evidence during the first decade of the 20th century but did not emerge in formalized theory until the mid-1900s.

The anti-mechanist's argument thus also requires that the human mind can always see whether or not a given formalized theory is consistent.

A formalized theory F is ω-consistent if it is not the case that for some formula A x), both F ⊢ ¬A(n) for all n, and F ⊢ ∃xA x).

Gödel originally only established the incompleteness of a particular though very comprehensive formalized theory P, a variant of Russell's type-theoretical system PM (for Principia Mathematica, see the sections on Paradoxes and Russell's Type Theories in the entries on type theory and Principia Mathematica), and all extension of P with the same language, whose set of axioms is primitive recursive.

Tarski mentions the extraordinary development of mathematical logic in recent decades, which had shown "how to present mathematical disciplines in the shape of formalized deductive theories" (Tarski 1983c, p. 409).

If this is read arithmetically, the direction from left to right is just the formalized version of Gödel's second incompleteness theorem: if a sufficiently strong formal theory T like Peano Arithmetic does not prove a contradiction, then it is not provable in T that T does not prove a contradiction.

Assume also that the world is infinite in size and that our formalized ideal theory T says it is.

On this model the result of "analysis" will be the definitions and primitive propositions or axioms from which the laws of a formalized scientfic theory can be derived by logical inference.

See also the supplement Zermelo-Fraenkel Set Theory for a formalized version of the axioms and further comments.

The proposed system is a symbolic representation, and is content-aware and can relate musical events to formalized concepts of Carnatic music theory.