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Publication details

Document type
Book chapters


Title
On some semi-constructive theories related to Kripke–Platek set theory

Participants in the publication
Fernando Ferreira (Author)
Dep. Matemática
CMAFcIO - Centro de Matemática, Aplicações Fundamentais e Investigação Operacional

Summary
We consider some very robust semi-constructive theories related to Kripke–Platek set theory, with and without the powerset operation. These theories include the law of excluded middle for bounded formulas, a form of Markov’s principle, the unrestricted collection scheme and, also, the classical contrapositive of the bounded collection scheme. We analyse these theories using forms of a functional interpretation which work in tandem with the constructible hierarchy (or the cumulative hierarchy, if the powerset operation is present). The main feature of these functional interpretations is to treat bounded quantifications as “computationally empty.” Our analysis is extended to a second-order setting enjoying some forms of class comprehension, including strict-11 reflection. The key idea of the extended analysis is to treat second-order (class) quantifiers as bounded quantifiers and strict-11 reflection as a form of collection. We will be able to extract some effective bounds from proofs in these systems in terms of the constructive tree ordinals up to the Bachmann–Howard ordinal.

Editor(s)
Gerhard Jaeger, Wilfried Sieg

Date of Publication
2017

Institution
FACULDADE DE CIÊNCIAS DA UNIVERSIDADE DE LISBOA

Where published
Feferman on Foundations

Publication Identifiers
ISSN - 2211-2758
eISSN - 2211-2766
ISBN - 9783319633329,9783319633343

Publisher
Springer International Publishing

Collection
Outstanding Contributions to Logic

Edition
1
Volume
13

Number of pages
38
Starting page
347
Last page
384

Document Identifiers
URL - http://dx.doi.org/10.1007/978-3-319-63334-3
DOI - https://doi.org/10.1007/978-3-319-63334-3

Keywords
Functional Interpretations Power Kripke-Platek set theory Strict pi-11 reflection Sigma-ordinal Intuitionistic Kripke-Platek set theory

Notes
This is a refereed research paper in mathematical logic. It is an invited paper to a volume of the collection "Outstanding Contributions to Logic" dedicated to the eminent logician Solomon Feferman.

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APA
Fernando Ferreira, (2017). On some semi-constructive theories related to Kripke–Platek set theory. Feferman on Foundations, 347-384

IEEE
Fernando Ferreira, "On some semi-constructive theories related to Kripke–Platek set theory" in Feferman on Foundations, 2017, pp. 347-384

BIBTEX
@incollection{39383, author = {Fernando Ferreira}, title = {On some semi-constructive theories related to Kripke–Platek set theory}, booktitle = {Feferman on Foundations}, year = 2017, pages = {347-384}, address = {}, publisher = {Springer International Publishing} }