TY - GEN

T1 - A minimal computational theory of a minimal computational universe

AU - Avron, Arnon

AU - Cohen, Liron

N1 - Publisher Copyright:
© Springer International Publishing AG 2018.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Computational theories

KW - Computational universes

KW - Formalized mathematics

KW - Rudimentary set theory

UR - http://www.scopus.com/inward/record.url?scp=85039420508&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-72056-2_3

DO - 10.1007/978-3-319-72056-2_3

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AN - SCOPUS:85039420508

SN - 9783319720555

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 37

EP - 54

BT - Logical Foundations of Computer Science - International Symposium, LFCS 2018, Proceedings

A2 - Nerode, Anil

A2 - Artemov, Sergei

PB - Springer Verlag

T2 - International Symposium on Logical Foundations of Computer Science, LFCS 2018

Y2 - 8 January 2018 through 11 January 2018

ER -