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Decidability and Specker sequences in intuitionistic mathematics

Mathematical Logic Quarterly, 2009
AbstractA bounded monotone sequence of reals without a limit is called a Specker sequence. In Russian constructive analysis, Church's Thesis permits the existence of a Specker sequence. In intuitionistic mathematics, Brouwer's Continuity Principle implies it is false that every bounded monotone sequence of real numbers has a limit.
Rasoul Ramezanian, Mohammad Ardeshir
exaly   +3 more sources

Reverse Mathematics and Completeness Theorems for Intuitionistic Logic

open access: yesNotre Dame Journal of Formal Logic, 2001
This article investigates the mathematical logic of intuitionistic propositional and predicate calculi using the framework of reverse mathematics [\textit{S. G. Simpson}, Subsystems of second order arithmetic, Berlin: Springer (1999; Zbl 0909.03048)]. Working in RCA\(_0\), the author shows that a version of the strong completeness theorem asserting the
exaly   +3 more sources

Mathematics of Intuitionistic Fuzzy Sets

Studies in Fuzziness and Soft Computing, 2016
Short firsthand remarks on the history and theory of Intuitionistic Fuzzy Sets (IFSs) are given. Influences of other areas of mathematics for development of the IFSs theory are discussed. On the basis of results in IFSs theory, some ideas for development of other mathematical areas are offered.
Krassimir Atanassov   +1 more
exaly   +2 more sources

Temporal and atemporal truth in intuitionistic mathematics

Topoi, 1994
In Sect. 11.2, we argue that the adoption of a tenseless notion of truth entails a realistic view of propositions and provability. This view, in turn, opens the way to the intelligibility of the classical meaning of the logical constants and consequently is incompatible with the antirealism of orthodox Intuitionism. In Sect.
Martino, Enrico, Usberti, Gabriele
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Intuitionistic mathematics does not needex falso quodlibet

Topoi, 1994
We define a system IR of first-order intuitionistic relevant logic. We show that intuitionistic mathematics (on the assumption that it is consistent) can be relevantized, by virtue of the following metatheorem: any intuitionistic proof of A from a setX of premisses can be converted into a proof in IR of eitherA or absurdity from some subset ofX.
Neil Tennant, Tennant Neil
exaly   +2 more sources

Intuitionistic mathematics and wittgenstein

History and Philosophy of Logic, 1991
The relation between Wittgenstein's philosophy of mathematics and mathematical Intuitionism has raised a considerable debate. My attempt is to analyse if there is a commitment in Wittgenstein to themes characteristic of the intuitionist movement in Mathematics and if that commitment is one important strain that runs through his Remarks on the ...
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Solipsism and philosophy of mathematics: intuitionists compared

2022
This paper will consider L. E. J. Brouwer, A. Heyting and G. F. C. Griss as the first generation of Dutch intuitionists to look at the interrelationship between solipsism and mathematics. In particular, our focus will be on Heyting, on the basis of the existence of some unpublished material (and also some difficult to find published material) revealing
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