Abstract
Existential statements seem to admit a constructive proof without countable choice only if the object to be constructed is uniquely determined, or is intended as an approximate solution of the problem in question. This conjecture is substantiated by re-examining some basic tools of mathematical analysis from a choice-free constructive point of view, starting from Dedekind cuts as an appropriate notion of real numbers. As a complement, the question whether densely defined continuous functions do approximate intermediate values is reduced to connectivity properties of the corresponding domains.
Key Words and Phrases
- Constructive Mathematics
- Countable Choice
- Unique Existence
- Approximate Analysis
- Intermediate Values
- Connectedness
2000 MSC
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Schuster, P.M. (2000). Elementary Choiceless Constructive Analysis. In: Clote, P.G., Schwichtenberg, H. (eds) Computer Science Logic. CSL 2000. Lecture Notes in Computer Science, vol 1862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44622-2_35
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