TY - GEN

T1 - A logical framework for developing and mechanizing set theories

AU - Avron, Arnon

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.

PY - 2016

Y1 - 2016

N2 - We describe a framework for formalizing mathematics which is based on the usual set theoretical foundations of mathematics. Its most important feature is that it reflects real mathematical practice in making an extensive use of statically defined abstract set terms, in the same way they are used in ordinary mathematical discourse. We also show how large portions of scientifically applicable mathematics can be developed in this framework in a straightforward way, using just rather weak set theories which are predicatively acceptable. The key property of those theories is that every object which is used in it is defined by some closed term of the theory. This allows for a very concrete, computationally-oriented interpretation. However, the development is not committed to such interpretation, and can easily be extended for handling stronger set theories, including ZFC itself.

AB - We describe a framework for formalizing mathematics which is based on the usual set theoretical foundations of mathematics. Its most important feature is that it reflects real mathematical practice in making an extensive use of statically defined abstract set terms, in the same way they are used in ordinary mathematical discourse. We also show how large portions of scientifically applicable mathematics can be developed in this framework in a straightforward way, using just rather weak set theories which are predicatively acceptable. The key property of those theories is that every object which is used in it is defined by some closed term of the theory. This allows for a very concrete, computationally-oriented interpretation. However, the development is not committed to such interpretation, and can easily be extended for handling stronger set theories, including ZFC itself.

UR - http://www.scopus.com/inward/record.url?scp=84976634941&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-40229-1_1

DO - 10.1007/978-3-319-40229-1_1

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AN - SCOPUS:84976634941

SN - 9783319402284

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

SP - 3

EP - 8

BT - Automated Reasoning - 8th International Joint Conference, IJCAR 2016, Proceedings

A2 - Olivetti, Nicola

A2 - Tiwari, Ashish

PB - Springer Verlag

T2 - 8th International Joint Conference on Automated Reasoning, IJCAR 2016

Y2 - 27 June 2016 through 2 July 2016

ER -