Non-deterministic inductive definitions

Archive for Mathematical Logic 52 (1-2):113-135 (2013)
  Copy   BIBTEX

Abstract

We study a new proof principle in the context of constructive Zermelo-Fraenkel set theory based on what we will call “non-deterministic inductive definitions”. We give applications to formal topology as well as a predicative justification of this principle.

Categories

Keywords

Reprint years

DOI

10.1007/s00153-012-0309-4

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 93,745

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Equivalents of the finitary non-deterministic inductive definitions.Ayana Hirata, Hajime Ishihara, Tatsuji Kawai & Takako Nemoto - 2019 - Annals of Pure and Applied Logic 170 (10):1256-1272.
Non-Deterministic Inductive Definitions and Fullness.Takako Nemoto & Hajime Ishihara - 2016 - In Peter Schuster & Dieter Probst (eds.), Concepts of Proof in Mathematics, Philosophy, and Computer Science. Boston: De Gruyter. pp. 163-170.
Mathematical proof theory in the light of ordinal analysis.Reinhard Kahle - 2002 - Synthese 133 (1/2):237 - 255.
Monotone inductive definitions in a constructive theory of functions and classes.Shuzo Takahashi - 1989 - Annals of Pure and Applied Logic 42 (3):255-297.
A class of higher inductive types in Zermelo‐Fraenkel set theory.Andrew W. Swan - 2022 - Mathematical Logic Quarterly 68 (1):118-127.
Inductively generated formal topologies.Thierry Coquand, Giovanni Sambin, Jan Smith & Silvio Valentini - 2003 - Annals of Pure and Applied Logic 124 (1-3):71-106.
On the formal points of the formal topology of the binary tree.Silvio Valentini - 2002 - Archive for Mathematical Logic 41 (7):603-618.
Induction–recursion and initial algebras.Peter Dybjer & Anton Setzer - 2003 - Annals of Pure and Applied Logic 124 (1-3):1-47.
The axiom of multiple choice and models for constructive set theory.Benno van den Berg & Ieke Moerdijk - 2014 - Journal of Mathematical Logic 14 (1):1450005.
The Relation Reflection Scheme.Peter Aczel - 2008 - Mathematical Logic Quarterly 54 (1):5-11.

Analytics

Added to PP
2013-10-27

Downloads
51 (#101,528)

6 months
5 (#1,552,255)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Benno Van Den Berg
University of Amsterdam

Citations of this work

Add more citations

References found in this work

Non-Well-Founded Sets.Peter Aczel - 1988 - Palo Alto, CA, USA: Csli Lecture Notes.
The strength of some Martin-Löf type theories.Edward Griffor & Michael Rathjen - 1994 - Archive for Mathematical Logic 33 (5):347-385.
Aspects of general topology in constructive set theory.Peter Aczel - 2006 - Annals of Pure and Applied Logic 137 (1-3):3-29.
Wellfounded trees in categories.Ieke Moerdijk & Erik Palmgren - 2000 - Annals of Pure and Applied Logic 104 (1-3):189-218.
Maximal and partial points in formal spaces.Erik Palmgren - 2006 - Annals of Pure and Applied Logic 137 (1-3):291-298.

View all 10 references / Add more references