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Natural density and probability, constructively

Publication date: 20.08.2020

Reports on Mathematical Logic, 2020, Number 55, pp. 41 - 59

https://doi.org/10.4467/20842589RM.20.002.12434

Authors

Samuele Maschio
Dipartimento di Matematica “Tullio Levi-Civita” Università di Padova, Italy
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Titles

Natural density and probability, constructively

Abstract

We give a constructive account of the frequentist approach to probability, by means of natural density. Then we discuss some probabilistic variants of the Limited Principle of Omniscience.

AMS Subject Classification: 03F65, 60A05.

References

[1] E. Bishop, D. S. Bridges, Constructive analysis, Springer 1985.

[2] D. Bridges, F. Richman, Varieties of Constructive Mathematics, Cambridge University Press 1987.

[3] Y.K. Chan, Notes on constructive probability theory, Ann. Probability 2 (1974), 51-75

[4] H. Ishihara, Reverse Mathematics in Bishop’s Constructive Mathematics, Philosophia Scientae (2006), 43–59.

[5] M.E. Maietti, A minimalist two-level foundation for constructive mathematics, Annals of Pure and Applied Logic 160:3 (2009), 319–354.

[6] M.E. Maietti, G. Sambin, Toward a minimalist foundation for constructive mathematics, In: From Sets and Types to Topology and Analysis: Practicable Foundations for Constructive Mathematics (Eds. L. Crosilla, P. Schuster), Oxford University Press 2005, pp. 91–114.

[7] I. Niven, The asymptotic density of sequences, Bull. Amer. Math. Soc. 6:11 (1951), 420–434

Information

Information: Reports on Mathematical Logic, 2020, Number 55, pp. 41 - 59

Article type: Original article

Titles:

Polish:

Natural density and probability, constructively

English:

Natural density and probability, constructively

Authors

Dipartimento di Matematica “Tullio Levi-Civita” Università di Padova, Italy

Published at: 20.08.2020

Received at: 19.02.2019

Accepted at: 26.06.2019

Article status: Open

Licence: CC BY-NC-ND  licence icon

Percentage share of authors:

Samuele Maschio (Author) - 100%

Article corrections:

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Publication languages:

English

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