David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 25 (5):559 - 565 (1996)
Let S be a deductive system such that S-derivability (⊦s) is arithmetic and sound with respect to structures of class K. From simple conditions on K and ⊦s, it follows constructively that the K-completeness of ⊦s implies MP(S), a form of Markov's Principle. If ⊦s is undecidable then MP(S) is independent of first-order Heyting arithmetic. Also, if ⊦s is undecidable and the S proof relation is decidable, then MP(S) is independent of second-order Heyting arithmetic, HAS. Lastly, when ⊦s is many-one complete, MP(S) implies the usual Markov's Principle MP. An immediate corollary is that the Tarski, Beth and Kripke weak completeness theorems for the negative fragment of intuitionistic predicate logic are unobtainable in HAS. Second, each of these: weak completeness for classical predicate logic, weak completeness for the negative fragment of intuitionistic predicate logic and strong completeness for sentential logic implies MP. Beth and Kripke completeness for intuitionistic predicate or sentential logic also entail MP. These results give extensions of the theorem of Gödel and Kreisel (in ) that completeness for pure intuitionistic predicate logic requires MP. The assumptions of Godel and Kreisel's original proof included the Axiom of Dependent Choice and Herbrand's Theorem, no use of which is explicit in the present article
|Keywords||intuitionistic logic completeness Markov's principle Kripke and Beth semantics|
|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
Stefano Berardi & Silvio Valentini (2004). Krivine's Intuitionistic Proof of Classical Completeness (for Countable Languages). Annals of Pure and Applied Logic 129 (1-3):93-106.
Robert Constable & Mark Bickford (2014). Intuitionistic Completeness of First-Order Logic. Annals of Pure and Applied Logic 165 (1):164-198.
Similar books and articles
Tatsuya Shimura (2000). Kripke Incompleteness of Predicate Extensions of the Modal Logics Axiomatized by a Canonical Formula for a Frame with a Nontrivial Cluster. Studia Logica 65 (2):237-247.
Linda Postniece, Combining Derivations and Refutations for Cut-Free Completeness in Bi-Intuitionistic Logic.
M. D. G. Swaen (1991). The Logic of First Order Intuitionistic Type Theory with Weak Sigma- Elimination. Journal of Symbolic Logic 56 (2):467-483.
Morten H. Sørensen & Paweł Urzyczyn (2010). A Syntactic Embedding of Predicate Logic Into Second-Order Propositional Logic. Notre Dame Journal of Formal Logic 51 (4):457-473.
Enrico Martino (1998). Negationless Intuitionism. Journal of Philosophical Logic 27 (2):165-177.
Franco Montagna & Hiroakira Ono (2002). Kripke Semantics, Undecidability and Standard Completeness for Esteva and Godo's Logic MTL∀. Studia Logica 71 (2):227-245.
Carl J. Posy (1982). A Free IPC is a Natural Logic: Strong Completeness for Some Intuitionistic Free Logics. Topoi 1 (1-2):30-43.
Dmitrij Skvortsov (1998). On Some Kripke Complete and Kripke Incomplete Intermediate Predicate Logics. Studia Logica 61 (2):281-292.
Yuichi Komori (1986). A New Semantics for Intuitionistic Predicate Logic. Studia Logica 45 (1):9 - 17.
Stefano Berardi (1999). Intuitionistic Completeness for First Order Classical Logic. Journal of Symbolic Logic 64 (1):304-312.
Added to index2009-01-28
Total downloads10 ( #140,553 of 1,096,601 )
Recent downloads (6 months)3 ( #99,452 of 1,096,601 )
How can I increase my downloads?