Address Mathematics and Statistics Dept. University of Helsinki PL 68 Helsinki 00014 Finland phone: +358403793969 (in Finland, 0403793969) Math Dept Fax: +358-9-19151400

Publications and Preprints

• {\em Fixed fee versus unit pricing for information goods: Competition, equilibria, and price wars}, with Peter C. Fishburn, Andrew M. Odlyzko, first appeared at FirstMonday online, [there] [here], and appeared in Internet Publishing and Beyond: The Economics of Digital Information and Intellectual Property, MIT Press, 167--189, 1997
• {\em Monotonic subsequences in dimensions higher than one}, with Andrew M. Odlyzko, James B. Shearer, [pdf], R14, Electronic Journal of Combinatorics, 4, 8pp, 2, 1997
• {\em Layered circlepackings and the type problem} [pdf], Proceedings American Math Society, 126, 3071-3074, 10, April 1998
• {\em Ordinal Computation}, [pdf] [ArXiv], 9pp, April 1998
• {\em Monotone subsequences in any dimension}, [acm] [pdf], Journal of Combinatorial Theory Series A, 85, 243-253, 2, 1999
• {\em Computing the Recursive Truth Predicate on Ordinal Register Machines}, with Peter Koepke, in {\em Logical Approaches to Computational Barriers, Second Conference on Computability in Europe, Swansea, UK}, [pdf], Arnold Beckmann, Ulrich Berger, Benedikt L\"owe, and John V Tucker, July 2006
• {\em Ehrenfeucht–-Fra\"iss\'e Games on Linear Orders}, in {\em Logic, Language, Information and Computation}, [pdf], Lecture Notes in Computer Science, 4576, 72-82, July 2007
• {\em Dynamic Ehrenfeucht-Fra\"iss\'e Games for strong logics over linear orders and other practical results}, [pdf], Reports in Mathematics and Statistics, University of Helsinki, 40pp, 486, November 2008
• {\em Minimality considerations for ordinal computers modeling constructibility}, with Peter Koepke, [pdf], Theoretical Computer Science, 394, 197-207, 2008
• {\em Register computations on ordinals}, with Peter Koepke, [pdf], Archive for Mathematical Logic, 47, 529-548, 6, September 2008
• {\em On linear order and computation}, [pdf], The National Library of Finland, National Library Network Services, E-thesis, 2008
• {\em On quantifier-rank equivalence between linear orders}, Submitted, accepted pending revisions’ review, Information and Computation, WOLLIC2007 post-conference volume