|Abstract||Using an axiomatization of second-order arithmetic (essentially second-order Peano Arithmetic without the Successor Axiom), arithmetic's basic operations are defined and its fundamental laws, up to unique prime factorization, are proven. Two manners of expressing a system's consistency are presented - the "Godel" consistency, where a wff is represented by a natural number, and the "real" consistency, where a wff is represented as a second-order sequence, which is a stronger notion. It is shown that the system can prove at least its Godel consistency and that closely allied systems can prove their real consistency|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Only published papers are available at libraries|
Similar books and articles
Dan E. Willard (2006). On the Available Partial Respects in Which an Axiomatization for Real Valued Arithmetic Can Recognize its Consistency. Journal of Symbolic Logic 71 (4):1189-1199.
Leszek Aleksander Kołodziejczyk (2006). On the Herbrand Notion of Consistency for Finitely Axiomatizable Fragments of Bounded Arithmetic Theories. Journal of Symbolic Logic 71 (2):624 - 638.
Added to index2009-01-28
Total downloads42 ( #31,695 of 722,867 )
Recent downloads (6 months)2 ( #36,757 of 722,867 )
How can I increase my downloads?