Intuitionistic axiomatizations for bounded extension Kripke models

被引：4
|
作者：
Ardeshir, M
Ruitenburg, W
Salehi, S
机构：
[1] Marquette Univ, Dept Math Stat & Comp Sci, Milwaukee, WI 53201 USA
[2] Sharif Univ Technol, Dept Math, Tehran, Iran
[3] Turku Univ, Dept Math, FIN-20014 Turku, Finland
来源：
ANNALS OF PURE AND APPLIED LOGIC | 2003年 / 124卷 / 1-3期
关键词：
completeness; Kripke model; Heyting arithmetic;
D O I：
10.1016/S0168-0072(03)00058-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present axiom systems, and provide soundness and strong completeness theorems, for classes of Kripke models with restricted extension rules among the node structures of the model. As examples we present an axiom system for the class of cofinal extension Kripke models, and an axiom system for the class of end-extension Kripke models. We also show that Heyting arithmetic (HA) is strongly complete for its class of end-extension models. Cofinal extension models of HA are models of Peano arithmetic (PA). (C) 2003 Elsevier B.V. All rights reserved.
引用
收藏
页码：267 / 285
页数：19
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