Analysis without actual infinity

Journal of Symbolic Logic 46 (3):625-633 (1981)
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Abstract

We define a first-order theory FIN which has a recursive axiomatization and has the following two properties. Each finite part of FIN has finite models. FIN is strong enough to develop that part of mathematics which is used or has potential applications in natural science. This work can also be regarded as a consistency proof of this hitherto informal part of mathematics. In FIN one can count every set; this permits one to prove some new probabilistic theorems

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Citations of this work

Theological Metaphors in Mathematics.Stanisław Krajewski - 2016 - Studies in Logic, Grammar and Rhetoric 44 (1):13-30.
Infinity and continuum in the alternative set theory.Kateřina Trlifajová - 2021 - European Journal for Philosophy of Science 12 (1):1-23.
Varieties of Finitism.Manuel Bremer - 2007 - Metaphysica 8 (2):131-148.
A Constructive Approach to Nonstandard Analysis.Erik Palmgren - 1995 - Annals of Pure and Applied Logic 73 (3):297-325.

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References found in this work

Foundations of Constructive Analysis.John Myhill - 1972 - Journal of Symbolic Logic 37 (4):744-747.
Undecidable Theories.Martin Davis - 1959 - Journal of Symbolic Logic 24 (2):167-169.
Handbook of Mathematical Logic.Akihiro Kanamori - 1984 - Journal of Symbolic Logic 49 (3):971-975.

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