Questions tagged [intuitionism]
The intuitionism tag has no usage guidance.
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Henkin-style completeness proofs for intuitionistic logic
Henkin-style completeness proofs are founded on a few basic presuppositions, such as the assumptions that the language of a logical theory must be enumerable (or at least that the axiom of choice ...
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Modal collapse upon addition of the law of the excluded middle to an Intuitionistic modal logic
Consider Propositional Lax Logic ($PLL$)
https://www.uni-bamberg.de/fileadmin/uni/fakultaeten/wiai_professuren/grundlagen_informatik/papersMM/pll.pdf
The Hilbert system of $PLL$ takes as axiom ...
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Alternatives to the law of the excluded middle
As a sentential logic, intuitionistic logic plus the law of the excluded middle gives classical logic.
Is there a logical law that is consistent with intuitionistic logic but inconsistent with ...
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Preserve validity between the two Kripke frames
The background of our discussion is intuitionistic logic, i.e. the following definitions are intuitionistic Kripke frame.
For $n \geq 1$, let $\mathcal{C}_n$ denote the frame which is shown in Fig.1. ...
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Going beyond the strength of Peano arithmetic "without sets"
First-order arithmetic is fairly weak, as measured for example by its consistency strength. When a stronger theory is desired, it is common to work with (fragments of) second-order arithmetic or set ...
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Is intuitionistic predicate logic (semantically) complete or incomplete?
According to Constructivism in Mathematics: An Introduction by Troelstra A.S. and Van Dalen (https://archive.org/details/constructivismin0002troe/page/718/mode/2up) it is proven in an intuitionisitc ...
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Subset Collection axiom
In Constructive Set Theory (CZF) the Power Set axiom is replaced with the Subset Collection axiom which I will state here:
$$ \exists c \forall u [\forall x \in a \exists y \in b (\psi(x,y,u)) \...