Vaught's theorem on axiomatizability by a scheme

Bulletin of Symbolic Logic 18 (3):382-402 (2012)
Abstract
In his 1967 paper Vaught used an ingenious argument to show that every recursively enumerable first order theory that directly interprets the weak system VS of set theory is axiomatizable by a scheme. In this paper we establish a strengthening of Vaught's theorem by weakening the hypothesis of direct interpretability of VS to direct interpretability of the finitely axiomatized fragment VS2 of VS. This improvement significantly increases the scope of the original result, since VS is essentially undecidable, but VS2 has decidable extensions. We also explore the ramifications of our work on finite axiomatizability of schemes in the presence of suitable comprehension principles
Keywords predicate logic   axiom   scheme
Categories (categorize this paper)
Options
 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: 9,360
External links
  •   Try with proxy.
  •   Try with proxy.
  •   Try with proxy.
  •   Try with proxy.
  • Through your library Configure
    References found in this work BETA

    No references found.

    Citations of this work BETA
    Similar books and articles
    Keith Hossack (2013). Sets and Plural Comprehension. Journal of Philosophical Logic:1-23.
    Robert L. Vaught (1967). Axiomatizability by a Schema. Journal of Symbolic Logic 32 (4):473-479.
    John P. Burgess (2010). Axiomatizing the Logic of Comparative Probability. Notre Dame Journal of Formal Logic 51 (1):119-126.
    Analytics

    Monthly downloads

    Sorry, there are not enough data points to plot this chart.

    Added to index

    2012-08-14

    Total downloads

    0

    Recent downloads (6 months)

    0

    How can I increase my downloads?

    My notes
    Sign in to use this feature


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