|
|
|
|
|
Lb's TheoremIn mathematical logic, Lb's theorem states that in a theory with Peano arithmetic, if it is provable that "if P is provable then P", then P is provable. Theorem First, Let mean that there exists a proof of in If a set of axioms is such that where PA are the Peano axioms of arithmetic, then for all sentences , if and only if Lb's theorem in provability logic Provability logic abstracts away from the details of encodings used in Gdel's incompleteness theorems by expressing the provability of in the given system in the language of modal logic, by means of the modality . Then we can formalize Lb's theorem by the axiom , known as axiom GL (for Gdel-Lb) (sometimes formalised by means of an inference rule that infers from ). The provability logic GL that results from taking the modal logic K4 and adding the above axiom GL is the most intensely investigated system in provability logic.
|
 |
|
| Copyright 2005-2009 OnPedia.com. All Rights Reserved |
|
|