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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeFeb 28th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexwe were lacking an entry _[[realizability]]_ that points to all the related entries (and in fact some entries were asking for just "realizability"). So I started one. Put in the following Idea-paragraph: > The idea of _realizability_ is essentially that of [[constructivism]], [[intuitionistic mathematics]] and the [[propositions as types]] paradigm: for instance constructively a [[proof]] of an [[existential quantification]] $\underset{x\in X}{\exists} \phi(x)$ consists of constructing a specific $x \in X$ and a proof of $\phi(x)$, which "realizes" the truth of the statement, whence the name ([e.g. Vermeeren 09, section 1](#Vermeeren09)).

   we were lacking an entry realizability that points to all the related entries (and in fact some entries were asking for just “realizability”).

   So I started one. Put in the following Idea-paragraph:

   The idea of realizability is essentially that of constructivism, intuitionistic mathematics and the propositions as types paradigm: for instance constructively a proof of an existential quantification $\underset{x\in X}{\exists} \phi(x)$ consists of constructing a specific $x \in X$ and a proof of $\phi(x)$, which “realizes” the truth of the statement, whence the name (e.g. Vermeeren 09, section 1).

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeFeb 28th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded some more canonical references

   added some more canonical references

3. • CommentRowNumber3.
   • CommentAuthorIngoBlechschmidt
   • CommentTimeMar 1st 2014
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   Author: IngoBlechschmidt
   Format: MarkdownItexAdded a reference to Andrej's lecture notes.

   Added a reference to Andrej’s lecture notes.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMar 1st 2014
   • (edited Mar 1st 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks! I already had this with more bibliographic information at _[[computable analysis]]_, but without the link to a pdf copy. Have merged the information now to: > [[Andrej Bauer]], _Realizability as connection between constructive and computable mathematics_, in T. Grubba, P. Hertling, H. Tsuiki, and [[Klaus Weihrauch]], (eds.) _CCA 2005 - Second International Conference on Computability and Complexity in Analysis_, August 25-29,2005, Kyoto, Japan, ser. Informatik Berichte, , vol. 326-7/2005. FernUniversität Hagen, Germany, 2005, pp. 378–379. ([pdf](http://math.andrej.com/data/c2c.pdf)) Also added this citation to _[[constructive mathematics]]_ and to _[[computability]]_ and cross-linked a bit more.

   Thanks! I already had this with more bibliographic information at computable analysis, but without the link to a pdf copy. Have merged the information now to:

   Andrej Bauer, Realizability as connection between constructive and computable mathematics, in T. Grubba, P. Hertling, H. Tsuiki, and Klaus Weihrauch, (eds.) CCA 2005 - Second International Conference on Computability and Complexity in Analysis, August 25-29,2005, Kyoto, Japan, ser. Informatik Berichte, , vol. 326-7/2005. FernUniversität Hagen, Germany, 2005, pp. 378–379. (pdf)

   Also added this citation to constructive mathematics and to computability and cross-linked a bit more.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMar 4th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexUpon request, Andrej Bauer kindly made available his text * _Intuitionistic Mathematics and Realizability in the Physical World_ ([web](http://math.andrej.com/2014/03/04/intuitionistic-mathematics-and-realizability-in-the-physical-world/), [pdf](http://math.andrej.com/wp-content/uploads/2014/03/real-world-realizability.pdf))

   Upon request, Andrej Bauer kindly made available his text

   • Intuitionistic Mathematics and Realizability in the Physical World (web, pdf)
6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeDec 10th 2020
   • (edited Dec 10th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded the full publication data for * [[Martin Hyland]], _Variations on realizability: realizing the propositional axiom of choice_, Mathematical Structures in Computer Science, Volume 12 , Issue 3 , June 2002 , pp. 295 - 317 ([doi:10.1017/S0960129502003651](https://doi.org/10.1017/S0960129502003651), [pdf](https://www.dpmms.cam.ac.uk/~martin/Research/Publications/2002/vor02.pdf)) <a href="https://ncatlab.org/nlab/revision/diff/realizability/18">diff</a>, <a href="https://ncatlab.org/nlab/revision/realizability/18">v18</a>, <a href="https://ncatlab.org/nlab/show/realizability">current</a>

   added the full publication data for

   • Martin Hyland, Variations on realizability: realizing the propositional axiom of choice, Mathematical Structures in Computer Science, Volume 12 , Issue 3 , June 2002 , pp. 295 - 317 (doi:10.1017/S0960129502003651, pdf)

   diff, v18, current

7. • CommentRowNumber7.
   • CommentAuthornLab edit announcer
   • CommentTimeJul 18th 2024
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexupdated link to Martin Hyland pdf Anonymouse <a href="https://ncatlab.org/nlab/revision/diff/realizability/21">diff</a>, <a href="https://ncatlab.org/nlab/revision/realizability/21">v21</a>, <a href="https://ncatlab.org/nlab/show/realizability">current</a>

   updated link to Martin Hyland pdf

   Anonymouse

   diff, v21, current