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BAR RECURSION AND PRODUCTS OF SELECTION FUNCTIONS

Published online by Cambridge University Press:  13 March 2015

MARTÍN ESCARDÓ  and
PAULO OLIVA
MARTÍN ESCARDÓ
Affiliation:
UNIVERSITY OF BIRMINGHAM, SCHOOL OF COMPUTER SCIENCE, BIRMINGHAM B15 2TT, UK
PAULO OLIVA
Affiliation:
QUEEN MARY UNIVERSITY OF LONDON, SCHOOL OF ELECTRONIC ENGINEERING AND COMPUTER SCIENCE, LONDON E1 4NS, UK
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Abstract

We show how two iterated products of selection functions can both be used in conjunction with system T to interpret, via the dialectica interpretation and modified realizability, full classical analysis. We also show that one iterated product is equivalent over system T to Spector’s bar recursion, whereas the other is T-equivalent to modified bar recursion. Modified bar recursion itself is shown to arise directly from the iteration of a different binary product of ‘skewed’ selection functions. Iterations of the dependent binary products are also considered but in all cases are shown to be T-equivalent to the iteration of the simple products.

Keywords

Spector bar recursionmodified bar recursionselection functiongeneralised quantifierT-definability
Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 1 , March 2015 , pp. 1 - 28
Copyright
Copyright © The Association for Symbolic Logic 2015 

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