Omega-consistency and the diamond

Studia Logica 39 (2-3):237 - 243 (1980)
G is the result of adjoining the schema (qAA)qA to K; the axioms of G* are the theorems of G and the instances of the schema qAA and the sole rule of G* is modus ponens. A sentence is -provable if it is provable in P(eano) A(rithmetic) by one application of the -rule; equivalently, if its negation is -inconsistent in PA. Let -Bew(x) be the natural formalization of the notion of -provability. For any modal sentence A and function mapping sentence letters to sentences of PA, inductively define A by: p = (p) (p a sentence letter); = ; (AB)su}= (A B); and (qA)= -Bew(A )(S) is the numeral for the Gödel number of the sentence S). Then, applying techniques of Solovay (Israel Journal of Mathematics 25, pp. 287–304), we prove that for every modal sentence A, G A iff for all , PA A ; and for every modal sentence A, G* A iff for all , A is true.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,357
External links
  • Through your library Configure
    References found in this work BETA
    M. H. Lob (1955). Solution of a Problem of Leon Henkin. Journal of Symbolic Logic 20 (2):115-118.
    Citations of this work BETA
    Similar books and articles

    Monthly downloads

    Added to index


    Total downloads

    9 ( #128,813 of 1,088,616 )

    Recent downloads (6 months)

    1 ( #69,601 of 1,088,616 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature

    Start a new thread
    There  are no threads in this forum
    Nothing in this forum yet.