The Quantiication Operator in Explicit Mathematics with Universes and Iterated Xed Point Theories with Ordinals

First steps into metapredicativity in explicit mathematics

Metapredicativity is a new general term in proof theory which describes the analysis and study of formal systems whose proof-theoretic strength is beyond the Feferman-Schütte ordinal Γ0 but which are nevertheless amenable to purely predicative methods. Typical examples of formal systems which are apt for scaling the initial part of metapredicativity are the transfinitely iterated fixed point th...

[To appear in: Annals of Pure and Applied Logic] Totality in applicative theories

In this paper we study applicative theories of operations and numbers with (and without) the non-constructive minimum operator in the context of a total application operation. We determine the proof-theoretic strength of such theories by relating them to well-known systems like Peano Arithmetic PA and the system ( 0 1 -CA) <" 0 of second order arithmetic. Essential use will be made of so-called...

The non-constructive mu operator, fixed point theories with ordinals, and the bar rule

APPROXIMATE FIXED POINT IN FUZZY NORMED SPACES FOR NONLINEAR MAPS

We de ne approximate xed point in fuzzy norm spaces and prove the existence theorems, we also consider approximate pair constructive map- ping and show its relation with approximate fuzzy xed point.

COUPLED FIXED POINT THEOREMS FOR RATIONAL TYPE CONTRACTIONS VIA C-CLASS FUNCTIONS

In this paper, by using C-class functions, we will present a coupled …xed problem in b-metric space for the single-valued operators satisfying a generalized contraction condition. First part of the paper is related to some …xed point theorems, the second part presents the uniqueness and existence for the solution of the coupled …xed point problem and in the third part we...