• J. D. Hamkins and D. E. Seabold, “Infinite time Turing machines with only one tape,” MLQ Math. Log. Q., vol. 47, iss. 2, pp. 271-287, 2001.  
  MR Citation arχiv

  @article{HamkinsSeabold2001:OneTape,
  AUTHOR = {Hamkins, Joel David and Seabold, Daniel Evan},
  TITLE = {Infinite time {T}uring machines with only one tape},
  JOURNAL = {MLQ Math. Log. Q.},
  FJOURNAL = {MLQ. Mathematical Logic Quarterly},
  VOLUME = {47},
  YEAR = {2001},
  NUMBER = {2},
  PAGES = {271--287},
  ISSN = {0942-5616},
  MRCLASS = {03D10 (68Q05)},
  MRNUMBER = {1829946 (2002f:03074)},
  MRREVIEWER = {Robert M. Baer},
  DOI = {10.1002/1521-3870(200105)47:2<271::AID-MALQ271>3.0.CO;2-6},
  URL = {http://dx.doi.org/10.1002/1521-3870(200105)47:2<271::AID-MALQ271>3.0.CO;2-6},
  eprint = {math/9907044}
  }

Infinite time Turing machines with only one tape are in many respects fully as powerful as their multi-tape cousins. In particular, the two models of machine give rise to the same class of decidable sets, the same degree structure and, at least for functions $f:\mathbb{R}\to\mathbb{N}$, the same class of computable functions. Nevertheless, there are infinite time computable functions $f:\mathbb{R}\to\mathbb{R}$ that are not one-tape computable, and so the two models of supertask computation are not equivalent. Surprisingly, the class of one-tape computable functions is not closed under composition; but closing it under composition yields the full class of all infinite time computable functions. Finally, every ordinal which is clockable by an infinite time Turing machine is clockable by a one-tape machine, except certain isolated ordinals that end gaps in the clockable ordinals.