Self-reference is a useful technical device in logical and foundational investigations and it is often the case that self-referential constructions give rise to fixed point theorems. We survey some applications thereof, mainly concerned with: (I) type-free abstraction with contraction-free logic; (II) theories of self-applicable operations based on combinatory logic and lambda calculus. The coda illustrates the non-trivial role of pure self-referential objects with an application to the constructive foundations of mathematics. with an application to the constructive foundations of mathematics.

Fixed point constructions / A. Cantini. - STAMPA. - (2006), pp. 27-52.

Fixed point constructions

CANTINI, ANDREA
2006

Abstract

Self-reference is a useful technical device in logical and foundational investigations and it is often the case that self-referential constructions give rise to fixed point theorems. We survey some applications thereof, mainly concerned with: (I) type-free abstraction with contraction-free logic; (II) theories of self-applicable operations based on combinatory logic and lambda calculus. The coda illustrates the non-trivial role of pure self-referential objects with an application to the constructive foundations of mathematics. with an application to the constructive foundations of mathematics.
2006
9781575865164
Self-Reference, CSLI Lecture Notes 178
27
52
A. Cantini
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/227641
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