David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Bulletin of Symbolic Logic 18 (3):382-402 (2012)
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)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Albert Visser (2014). Peano Corto and Peano Basso: A Study of Local Induction in the Context of Weak Theories. Mathematical Logic Quarterly 60 (1-2):92-117.
Similar books and articles
Dmitrij Skvortsov (1997). Not Every "Tabular" Predicate Logic is Finitely Axiomatizable. Studia Logica 59 (3):387-396.
Sachio Hirokawa (1992). The Converse Principal Type-Scheme Theorem in Lambda Calculus. Studia Logica 51 (1):83 - 95.
Janusz Czelakowski (1985). Algebraic Aspects of Deduction Theorems. Studia Logica 44 (4):369 - 387.
Victor Harnik & Michael Makkai (1976). Applications of Vaught Sentences and the Covering Theorem. Journal of Symbolic Logic 41 (1):171-187.
Steven Buechler (1988). The Classification of Small Weakly Minimal Sets. II. Journal of Symbolic Logic 53 (2):625-635.
W. Craig & R. L. Vaught (1958). Finite Axiomatizability Using Additional Predicates. Journal of Symbolic Logic 23 (3):289-308.
J. Czelakowski & W. Dziobiak (1999). Deduction Theorems Within RM and its Extensions. Journal of Symbolic Logic 64 (1):279-290.
Keith Hossack (2014). Sets and Plural Comprehension. Journal of Philosophical Logic 43 (2-3):517-539.
Robert L. Vaught (1967). Axiomatizability by a Schema. Journal of Symbolic Logic 32 (4):473-479.
Jeffry L. Hirst (1999). Ordinal Inequalities, Transfinite Induction, and Reverse Mathematics. Journal of Symbolic Logic 64 (2):769-774.
John P. Burgess (2010). Axiomatizing the Logic of Comparative Probability. Notre Dame Journal of Formal Logic 51 (1):119-126.
Paul C. Gilmore (1986). Natural Deduction Based Set Theories: A New Resolution of the Old Paradoxes. Journal of Symbolic Logic 51 (2):393-411.
Olivier Esser (2000). Inconsistency of the Axiom of Choice with the Positive Theory GPK+ ∞. Journal of Symbolic Logic 65 (4):1911 - 1916.
Sorry, there are not enough data points to plot this chart.
Added to index2012-08-14
Total downloads1 ( #484,330 of 1,413,434 )
Recent downloads (6 months)1 ( #154,636 of 1,413,434 )
How can I increase my downloads?