On strong provability predicates and the associated modal logics

1993 ◽  
Vol 58 (1) ◽  
pp. 249-290 ◽  
Author(s):  
Konstantin N. Ignatiev
Keyword(s):  
Fixed Point ◽  
Peano Arithmetic ◽  
Modal Logics ◽  
Fixed Point Property ◽  
Provability Logic ◽  
Point Property ◽  
Craig Interpolation ◽  
Modal Properties ◽  
Craig Interpolation Lemma

AbstractPA is Peano Arithmetic. Pr(x) is the usual Σ1,-formula representing provability in PA. A strong provability predicate is a formula which has the same properties as Pr(·) but is not Σ1. An example: Q is ω-provable if PA + ¬Q is ω-inconsistent (Boolos [4]). In [5] Dzhaparidze introduced a joint provability logic for iterated ω-provability and obtained its arithmetical completeness.In this paper we prove some further modal properties of Dzhaparidze's logic, e.g., the fixed point property and the Craig interpolation lemma. We also consider other examples of the strong provability predicates and their applications.

scholarly journals Brush spaces and the fixed point property

2011 ◽  
Vol 158 (8) ◽  
pp. 1085-1089 ◽  
Author(s):  
M.M. Marsh ◽  
J.R. Prajs
Keyword(s):  
Fixed Point ◽  
Fixed Point Property ◽  
Point Property

scholarly journals Towards the fixed point property for superreflexive spaces

2001 ◽  
Vol 64 (3) ◽  
pp. 435-444 ◽  
Author(s):  
Andrzej Wiśnicki
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Unit Sphere ◽  
Convex Set ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property ◽  
Geometrical Condition

A Banach space X is said to have property (Sm) if every metrically convex set A ⊂ X which lies on the unit sphere and has diameter not greater than one can be (weakly) separated from zero by a functional. We show that this geometrical condition is closely connected with the fixed point property for nonexpansive mappings in superreflexive spaces.

scholarly journals A product space with the fixed point property

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Helga Fetter Nathansky ◽  
Enrique Llorens-Fuster
Keyword(s):  
Fixed Point ◽  
Product Space ◽  
Fixed Point Property ◽  
Point Property

Order Extensions and the Fixed Point Property

Order ◽  
2008 ◽  
Vol 25 (3) ◽  
pp. 267-279
Author(s):  
Imed Zaguia
Keyword(s):  
Fixed Point ◽  
Fixed Point Property ◽  
Point Property

scholarly journals James quasi reflexive space has the fixed point property

1989 ◽  
Vol 39 (1) ◽  
pp. 25-30 ◽  
Author(s):  
M.A. Khamsi
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Unconditional Basis ◽  
Fixed Point Property ◽  
Point Property ◽  
Reflexive Space ◽  
Lin's Method ◽  
Lin’S Method

We prove that the classical sequence James space has the fixed point property. This gives an example of Banach space with a non-unconditional basis where the Maurey-Lin's method applies.

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