User paulo oliva - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T21:56:35Z http://mathoverflow.net/feeds/user/22450 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/61134/looking-for-papers-and-articles-on-the-tarskian-moglichkeit/92409#92409 Answer by Paulo Oliva for Looking for papers and articles on the Tarskian Möglichkeit Paulo Oliva 2012-03-27T20:20:52Z 2012-03-27T20:20:52Z <p>Rob, I didn't know this was called the Tarskian Möglichkeit, but Martin Escardo and I have been studying this operator (A -> B) -> A, in the more general case when falsity is an arbitrary formula B, for the past few years, mainly in connection with computational interpretations of classical theorems. If we let B be fixed, then we define</p> <p>J A = (A -> B) -> A</p> <p>It is easy to show that this is a strong monad. We call it the "selection monad" or the "Peirce monad", as J A -> A is Peirce's law. In fact, the seemingly absurd theorem you mentioned in your post is the cornerstone for our work on interpreting ineffective principles such as the Tychonoff theorem, for instance. Have a look at some of our papers, e.g.</p> <p>Martín Escardó and Paulo Oliva. Sequential games and optimal strategies. Proceedings of the Royal Society A, 467:1519-1545, 2011.</p> <p>Martín Escardó Paulo Oliva, The Pierce translation. Annals of Pure and Applied Logic, 163(6):681-692, 2012.</p> <p>Or others found on our webpages: <a href="http://www.eecs.qmul.ac.uk/~pbo/" rel="nofollow">http://www.eecs.qmul.ac.uk/~pbo/</a></p> <p>Any paper which mentions "selection functions" or "game" is related to the operator you are asking about.</p> <p>I must warn we have been studying this operator in the setting of intuitonistic (minimal) logic. But I find it very interesting that you are looking at this in the more refined (substructural) settings of linear logic and Lukasiewicz logic.</p> <p>Best regards, Paulo.</p>