Some notes on the superintuitionistic logic of chequered subsets of ${\sf R}^\infty$ (bibtex)

by Tadeusz Litak

Reference:

Tadeusz Litak: Some notes on the superintuitionistic logic of chequered subsets of ${\sf R}^\infty$, In Bulletin of the Section of Logic, 33(2), pp. 81–86, 2004. The paper studies superintuitionistic version of the logic of chequered subsets introduced by Johan van Benthem, Guram Bezhanishvili and Mai Gehrke. It is observed that this logic possesses the disjunction property, contains the Scott axiom, fails to contain the Kreisel-Putnam axiom and is not structurally complete. It is also a sublogic of the Medvedev logic ML. Very interesting follow-up results have been obtained by Gaelle Fontaine and Timofei Shatrov. The latter claimed to have settled negatively the issue of finite axiomatizably of Cheq; however, to the best of my knowledge, this has never been published. The local copy is slightly extended; in particular, the proof of main theorem is hopefully more readable: [local copy]

Bibtex Entry:

@article{Litak04:bsl,
  title={Some notes on the superintuitionistic logic of chequered subsets of ${\sf R}^\infty$},
  author={Litak, Tadeusz},
  journal={Bulletin of the Section of Logic},
  volume={33},
  number={2},
  pages={81--86},
  url = {https://arxiv.org/abs/1808.06393},
  ALTurl = {http://www.filozof.uni.lodz.pl/bulletin/pdf/33_2_2.pdf},
  year={2004},
  comment = {<div class="abstract"> The paper studies superintuitionistic version of the logic of chequered subsets introduced by <a href="http://dx.doi.org/10.1023/B\%3ASTUD.0000009564.00287.16">Johan van Benthem, Guram Bezhanishvili and Mai Gehrke</a>.  It is observed  that this logic possesses
  the disjunction property, contains the Scott axiom, fails to  contain the
  Kreisel-Putnam axiom and is not structurally complete.  It is also a sublogic of the Medvedev logic
  ML.  </div> <div class="textleft">
Very interesting
follow-up results have been obtained by <a href="http://www.aiml.net/volumes/volume6/Fontaine.ps">Gaelle Fontaine</a> and <a href="http://atlas-conferences.com/cgi-bin/abstract/caug-46">Timofei Shatrov</a>. The latter  claimed to have settled negatively the issue of finite axiomatizably of Cheq; however, to the best of my knowledge, this has never been published. The local copy is slightly extended; in particular, the
proof of main theorem is hopefully more readable: </div> <a href="http://www8.cs.fau.de/~litak/papers/euclidean2018.pdf"> [local copy] </a>}
}