In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans. That is, given a set of axioms, the only propositions that can exist are those that ...

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Do De Morgan's laws hold in propositional intuitionistic logic?

In Wikipedia page on intuitionistic logic, it is stated that excluded middle and double negation elimination are not axioms. Does this mean that De Morgan's laws, stated $$ \lnot (p \land q) \iff ...
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Understanding a proof of Diaconescu's theorem

I am trying to walk through the proof of Diaconescu's theorem that the axiom of choice implies the law of excluded middle at http://plato.stanford.edu/entries/intuitionism/#ChoAxi. To paraphrase: ...
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Defining “Penon Infinitesimals”.

In this lecture (which is accompanied by these slides), right near the end (so page 9 in the pdf of the slides; I don't think you have to watch the lecture), P. Johnstone refers to the "Penon ...
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Contraposition in intuitionistic logic?

I read that contraposition $\neg Q \rightarrow \neg P$ in intuitionistic logic is not generally equivalent to $P \rightarrow Q$. If this is right, in what case can this contraposition ...
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How is Goedel's 1st incompleteness theorem related to the Axioms of a theory

i am thinking of various connections and formulations of Goedel's 1st incompleteness theorem. Apart from connections to Turing's Halting Problem and Algorithmic Complexity Theory, i am looking for ...