A minimal computational theory of a minimal computational universe

Arnon Avron, Liron Cohen*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In [3] a general logical framework for formalizing set theories of different strength was suggested. We here employ that framework, focusing on the exploration of computational theories. That is, theories whose set of closed terms suffices for denoting every concrete set (including infinite ones) that might be needed in applications, as well as for computations with sets. We demonstrate that already the minimal computational level of the framework, in which only a minimal computational theory and a minimal computational universe are employed, suffices for developing large portions of scientifically applicable mathematics.

Original languageEnglish
Title of host publicationLogical Foundations of Computer Science - International Symposium, LFCS 2018, Proceedings
EditorsAnil Nerode, Sergei Artemov
PublisherSpringer Verlag
Pages37-54
Number of pages18
ISBN (Print)9783319720555
DOIs
StatePublished - 2018
EventInternational Symposium on Logical Foundations of Computer Science, LFCS 2018 - [state] FL, United States
Duration: 8 Jan 201811 Jan 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10703 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceInternational Symposium on Logical Foundations of Computer Science, LFCS 2018
Country/TerritoryUnited States
City[state] FL
Period8/01/1811/01/18

Funding

FundersFunder number
Weizmann Institute of Science – National Postdoctoral Award program for Advancing Women in Science
Weizmann Institute of Science

    Keywords

    • Computational theories
    • Computational universes
    • Formalized mathematics
    • Rudimentary set theory

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