PP-2008-32: Bilkova, Marta and de Jongh, Dick and Joosten, Joost J. (2008) Interpretability in PRA. [Report]
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Abstract
In this paper we study IL(PRA), the interpretability logic of PRA. As
PRA is neither an essentially reflexive theory nor finitely
axiomatizable, the two known arithmetical completeness results do not
apply to PRA: IL(PRA) is not ILM or ILP. IL(PRA) does of course
contain all the principles known to be part of IL(All), the
interpretability logic of the principles common to all reasonable
arithmetical theories. In this paper, we take two arithmetical
properties of PRA and see what their consequences in the modal logic
IL(PRA) are. These properties are reflected in the so-called
Beklemishev Principle $B$, and Zambella’s Principle $Z$, neither of
which is a part of IL(All). Both principles and their interrelation
are submitted to a modal study. In particular, we prove a frame
condition for $B$. morover, we prove that $Z$ follows from a
restricted form of $B$. Finally, we give an overview of the known
relationships of IL(PRA) to important other interpetability
principles.
| Item Type: | Report |
|---|---|
| Report Nr: | PP-2008-32 |
| Series Name: | Prepublication (PP) Series |
| Year: | 2008 |
| Uncontrolled Keywords: | interpetability; arithmetic |
| Depositing User: | Prof. Dick de Jongh |
| Date Deposited: | 12 Oct 2016 14:37 |
| Last Modified: | 12 Oct 2016 14:37 |
| URI: | https://eprints.illc.uva.nl/id/eprint/306 |
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