Questions tagged [intuitionism]

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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 ...
Bruno Bentzen's user avatar
3 votes
2 answers
317 views

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 ...
user65526's user avatar
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34 votes
3 answers
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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 ...
Colin Tan's user avatar
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6 votes
1 answer
197 views

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. ...
mahu's user avatar
  • 63
4 votes
1 answer
804 views

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 ...
Robin Saunders's user avatar
4 votes
0 answers
312 views

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 ...
ToucanIan's user avatar
  • 391
3 votes
1 answer
295 views

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)) \...
ToucanIan's user avatar
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