Mathematical Logic Quarterly 48 (1):157-160 (2002)

Authors
Abstract
In the first section of this paper we show that i Π1 ≡ W⌝⌝lΠ1 and that a Kripke model which decides bounded formulas forces iΠ1 if and only if the union of the worlds in any path in it satisflies IΠ1. In particular, the union of the worlds in any path of a Kripke model of HA models IΠ1. In the second section of the paper, we show that for equivalence of forcing and satisfaction of Πm-formulas in a linear Kripke model deciding Δ0-formulas it is necessary and sufficient that the model be Σm-elementary. This implies that if a linear Kripke model forces PEMprenex, then it forces PEM. We also show that, for each n ≥ 1, iΦn does not prove ℋ(IΠn's are Burr's fragments of HA
Keywords Kripke models  fragments of Heyting Arithmetic
Categories (categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
External links

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

Fragments of $HA$ Based on $\Sigma_1$ -Induction.Kai F. Wehmeier - 1997 - Archive for Mathematical Logic 37 (1):37-49.
Intuitionistic Validity in T-Normal Kripke Structures.Samuel R. Buss - 1993 - Annals of Pure and Applied Logic 59 (3):159-173.
Fragments of Heyting Arithmetic.Wolfgang Burr - 2000 - Journal of Symbolic Logic 65 (3):1223-1240.
Classical and Intuitionistic Models of Arithmetic.Kai F. Wehmeier - 1996 - Notre Dame Journal of Formal Logic 37 (3):452-461.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Corrigendum to "Weak Arithmetics and Kripke Models".Morteza Moniri - 2004 - Mathematical Logic Quarterly 50 (6):637.
Intuitionistic Weak Arithmetic.Morteza Moniri - 2003 - Archive for Mathematical Logic 42 (8):791-796.
Classical and Intuitionistic Models of Arithmetic.Kai F. Wehmeier - 1996 - Notre Dame Journal of Formal Logic 37 (3):452-461.
On the Structure of Kripke Models of Heyting Arithmetic.Zoran Marković - 1993 - Mathematical Logic Quarterly 39 (1):531-538.
Submodels of Kripke Models.Albert Visser - 2001 - Archive for Mathematical Logic 40 (4):277-295.
Homomorphisms and Chains of Kripke Models.Morteza Moniri & Mostafa Zaare - 2011 - Archive for Mathematical Logic 50 (3-4):431-443.
A Note on Recursive Models of Set Theories.Domenico Zambella & Antonella Mancini - 2001 - Notre Dame Journal of Formal Logic 42 (2):109-115.
Nonstandard Models and Kripke's Proof of the Gödel Theorem.Hilary Putnam - 2000 - Notre Dame Journal of Formal Logic 41 (1):53-58.
Theories of Arithmetics in Finite Models.Michał Krynicki & Konrad Zdanowski - 2005 - Journal of Symbolic Logic 70 (1):1-28.
Models of Intuitionistic TT and N.Daniel Dzierzgowski - 1995 - Journal of Symbolic Logic 60 (2):640-653.
Kripke Semantics for Provability Logic GLP.Lev D. Beklemishev - 2010 - Annals of Pure and Applied Logic 161 (6):756-774.

Analytics

Added to PP index
2013-12-01

Total views
45 ( #213,613 of 2,348,958 )

Recent downloads (6 months)
4 ( #186,326 of 2,348,958 )

How can I increase my downloads?

Downloads

My notes