David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 56 (2):467-483 (1991)
Via the formulas-as-types embedding certain extensions of Heyting Arithmetic can be represented in intuitionistic type theories. In this paper we discuss the embedding of ω-sorted Heyting Arithmetic HA ω into a type theory WL, that can be described as Troelstra's system ML 1 0 with so-called weak Σ-elimination rules. By syntactical means it is proved that a formula is derivable in HA ω if and only if its corresponding type in WL is inhabited. Analogous results are proved for Diller's so-called restricted system and for a type theory based on predicate logic instead of arithmetic
|Keywords||No keywords specified (fix it)|
|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
No citations found.
Similar books and articles
Branislav R. Boričić (1986). A Cut-Free Gentzen-Type System for the Logic of the Weak Law of Excluded Middle. Studia Logica 45 (1):39 - 53.
D. C. McCarty (1996). Undecidability and Intuitionistic Incompleteness. Journal of Philosophical Logic 25 (5):559 - 565.
W. W. Tait (2003). The Completeness of Heyting First-Order Logic. Journal of Symbolic Logic 68 (3):751-763.
Mitsuhiro Okada (1987). A Weak Intuitionistic Propositional Logic with Purely Constructive Implication. Studia Logica 46 (4):371 - 382.
Itay Ben-Yaacov & Frank O. Wagner (2004). On Almost Orthogonality in Simple Theories. Journal of Symbolic Logic 69 (2):398 - 408.
G. Mints (1999). Cut-Elimination for Simple Type Theory with an Axiom of Choice. Journal of Symbolic Logic 64 (2):479-485.
Jonathan P. Seldin (2000). On the Role of Implication in Formal Logic. Journal of Symbolic Logic 65 (3):1076-1114.
Daniel Dzierzgowski (1995). Models of Intuitionistic TT and N. Journal of Symbolic Logic 60 (2):640-653.
M. D. G. Swaen (1992). A Characterization of ML in Many-Sorted Arithmetic with Conditional Application. Journal of Symbolic Logic 57 (3):924 - 953.
Added to index2009-01-28
Total downloads5 ( #230,090 of 1,102,976 )
Recent downloads (6 months)2 ( #183,254 of 1,102,976 )
How can I increase my downloads?