\ifx\undefined\bysame
\newcommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\,}
\fi
\begin{thebibliography}{AxKo65b}

\bibitem[AxKo65a]{AxKo65a}
J.~Ax and S.~Kochen, {\em Diophantine problems over local fields, {I}}, Amer.
  J. Math. {\bf 87} (1965), 605--630.

\bibitem[AxKo65b]{AxKo65b}
J.~Ax and S.~Kochen, {\em Diophantine problems over local fields, {II}: {A}
  complete set of axioms for $p$-adic number theory}, Amer. J. Math. {\bf 87}
  (1965), 631--648.

\bibitem[AxKo66]{AxKo66}
J.~Ax and S.~Kochen, {\em Diophantine problems over local fields, {III}:
  {D}ecidable fields}, Ann. of Math. (2) {\bf 83} (1966), 437--456.

\bibitem[Bak83]{Bak83}
K.A. Baker, {\em Strong shift equivalence of $2\times 2$ matrices of
  nonnegative integers}, Ergodic Theory Dynamical Systems {\bf 3} (1983),
  501--508.

\bibitem[Bak87]{Bak87}
K.A. Baker, {\em Strong shift equivalence and shear adjacency of nonnegative
  square integer matrices}, Linear Algebra Appl. {\bf 93} (1987), 131--147.

\bibitem[BJKR98]{BJKR98}
O.~Bratteli, P.E.T. Jorgensen, K.H. Kim, and F.~Roush, {\em Non-stationarity of
  isomorphism between {AF} algebras defined by stationary {B}ratteli diagrams},
  Ergodic Theory Dynam. Systems, to appear.

\bibitem[BJO99]{BJO99}
O.~Bratteli, P.E.T. Jorgensen, and V.~Ostrovs'ky\u{\i}, {\em Representation
  theory and numerical {AF}-in\-vari\-ants: {T}he representations and
  centralizers of certain states on $\mathcal{O}_{d}$}, submitted to Mem.\
  Amer.\ Math.\ Soc.

\bibitem[Bla86]{Bla86}
B.~Blackadar, {\em ${K}$-theory for {O}perator {A}lgebras}, MSRI Publication
  Series, vol.~5, Springer-Verlag, New York--Heidelberg--Berlin--Tokyo, 1986.

\bibitem[BMT87]{BMT87}
M.~Boyle, B.~Marcus, and P.~Trow, {\em Resolving maps and the dimension group
  for shifts of finite type}, Mem. Amer. Math. Soc. {\bf 70} (1987), no.~377.

\bibitem[BoHa91]{BoHa91}
M.~Boyle and D.~Handelman, {\em The spectra of nonnegative matrices via
  symbolic dynamics}, Ann. of Math. (2) {\bf 133} (1991), 249--316.

\bibitem[BoHa93]{BoHa93}
M.~Boyle and D.~Handelman, {\em Algebraic shift equivalence and primitive
  matrices}, Trans. Amer. Math. Soc. {\bf 336} (1993), 121--149.

\bibitem[BoSh66]{BoSh66}
Z.I. Borevich and I.R. Shafarevich, {\em Number {T}heory}, Pure and Applied
  Mathematics, vol.~20, Academic Press, New York--London, 1966, translated from
  the Russian {\cyr Teoriya Chisel}, Moscow, 1964, by N. Greenleaf.

\bibitem[Bra72]{Bra72}
O.~Bratteli, {\em Inductive limits of finite dimensional ${C}^*$-al\-ge\-bras},
  Trans. Amer. Math. Soc. {\bf 171} (1972), 195--234.

\bibitem[Buc86]{Buc86}
J.~Buchmann, {\em Generalized {C}ontinued {F}ractions and {N}umber {T}heoretic
  {C}omputations}, Berichte der Mathematisch-Statistischen Sektion in der
  Forschungsgesellschaft Joanneum, vol. 269, Forschungszentrum Graz
  Mathematisch-Statistische Sektion, Graz, 1986, Paper from the sixteenth
  Styrian mathematical symposium held in Stift Rein/Graz, September 21--26,
  1986.

\bibitem[CaEi56]{CaEi56}
H.P. Cartan and S.~Eilenberg, {\em Homological {A}lgebra}, Princeton University
  Press, Princeton, New Jersey, 1956.

\bibitem[CuKr80]{CuKr80}
J.~Cuntz and W.~Krieger, {\em Topological {M}arkov chains with dicyclic
  dimension groups}, J. Reine Angew. Math. {\bf 320} (1980), 44--51.

\bibitem[DHS99]{DHS99}
F.~Durand, B.~Host, and S.~Skau, {\em Substitutional dynamical systems,
  {B}ratteli diagrams, and dimension groups}, Ergodic Theory Dynam. Systems
  {\bf 19} (1999), 953--993.

\bibitem[DMR76]{DMR76}
M.~Davis, Yu. Matijasevi{\v{c}}, and J.~Robinson, {\em Hilbert's tenth problem:
  {D}iophantine equations: positive aspects of a negative solution},
  Mathematical {D}evelopments {A}rising from {H}ilbert {P}roblems (De Kalb,
  Ill., 1974) (F.E. Browder, ed.), Proceedings of Symposia in Pure Mathematics,
  vol.~28, American Mathematical Society, Providence, 1976, pp.~323--378.

\bibitem[Eff81]{Eff81}
E.G. Effros, {\em Dimensions and ${C}\sp{\ast} $-algebras}, CBMS Regional Conf.
  Ser. in Math., vol.~46, Conference Board of the Mathematical Sciences,
  Washington, 1981.

\bibitem[Ell76]{Ell76}
G.A. Elliott, {\em On the classification of inductive limits of sequences of
  semisimple finite-dimensional algebras}, J. Algebra {\bf 38} (1976), 29--44.

\bibitem[Ell79]{Ell79}
G.A. Elliott, {\em On totally ordered groups, and ${K}_{0}$}, Ring theory
  (Waterloo, 1978) (D.~Handelman and J.~Lawrence, eds.), Lecture Notes in
  Math., vol. 734, Springer, Berlin, 1979, pp.~1--49.

\bibitem[GrSe80a]{GrSe80a}
F.~Grunewald and D.~Segal, {\em Some general algorithms, {I}: {A}rithmetic
  groups}, Ann. of Math. (2) {\bf 112} (1980), 531--583.

\bibitem[GrSe80b]{GrSe80b}
F.~Grunewald and D.~Segal, {\em Some general algorithms, {II}: {N}ilpotent
  groups}, Ann. of Math. (2) {\bf 112} (1980), 585--617.

\bibitem[GrSe82]{GrSe82}
F.~Grunewald and D.~Segal, {\em R\'esolution effective de quelques probl\`emes
  diophantiens sur les groupes alg\'ebriques lin\'eaires}, C. R. Acad. Sci.
  Paris Ser. I Math. {\bf 295} (1982), 479--481.

\bibitem[Han81]{Han81}
D.~Handelman, {\em Positive matrices and dimension groups affiliated to
  ${C}^*$-algebras and topological {M}arkov chains}, J.~Operator Theory {\bf 6}
  (1981), 55--74.

\bibitem[Han87]{Han87}
D.~Handelman, {\em Eventually positive matrices with rational eigenvectors},
  Ergodic Theory Dynamical Systems {\bf 7} (1987), 193--196.

\bibitem[Her69]{Her69}
Hans Hermes, {\em Enumerability, {D}ecidability, {C}omputability: {A}n
  {I}ntroduction to the {T}heory of {R}ecursive {F}unctions}, Springer-Verlag,
  New York, 1969, Translated from the German by G. T. Hermann and O. Plassmann.
  Second revised edition. Die Grundlehren der mathematischen Wissenschaften,
  Band 127.

\bibitem[Her78]{Her78}
Hans Hermes, {\em Aufz\"ahlbarkeit, {E}ntscheidbarkeit, {B}erechenbarkeit:
  {E}inf\"uhrung in die {T}heorie der rekursiven {F}unktionen}, third ed.,
  Springer-Verlag, Berlin, 1978.

\bibitem[HiSi00]{HiSi00}
M.~Hindry and J.H. Silverman, {\em Diophantine {G}eometry: An {I}ntroduction},
  Graduate Texts in Mathematics, vol. 201, Springer-Verlag, New York, 2000.

\bibitem[Jac75]{Jac75}
N.~Jacobson, {\em Lectures in {A}bstract {A}lgebra, {V}ol.~{III}: Theory of
  fields and {G}alois theory}, Graduate Texts in Mathematics, vol.~32,
  Springer-Verlag, New York--Heidelberg, 1975, second corrected printing.

\bibitem[Jac97]{Jac97}
J.~Jacklitch, {\em Homeomorphisms of $1$-dimensional hyperbolic attractors},
  thesis preprint, 1997.

\bibitem[KaMa51]{KaMa51}
I.~Kaplansky and G.W. Mackey, {\em A generalization of {U}lm's theorem}, Summa
  Brasil. Math. 2 (1951), 195--202.

\bibitem[Kap69]{Kap69}
I.~Kaplansky, {\em Infinite {A}belian {G}roups}, revised ed., The University of
  Michigan Press, Ann Arbor, 1969.

\bibitem[KiRo79]{KiRo79}
K.H. Kim and F.W. Roush, {\em Some results on decidability of shift
  equivalence}, J. Combin. Inform. System Sci. {\bf 4} (1979), 123--146.

\bibitem[KiRo88]{KiRo88}
K.H. Kim and F.W. Roush, {\em Decidability of shift equivalence}, Dynamical
  {S}ystems (College Park, MD, 1986--87) (J.C. Alexander, ed.), Lecture Notes
  in Mathematics, vol. 1342, Springer-Verlag, Berlin-New York, 1988,
  pp.~374--424.

\bibitem[Kit98]{Kit98}
B.P. Kitchens, {\em Symbolic {D}ynamics: One-sided, {T}wo-sided and {C}ountable
  {S}tate {M}arkov {S}hifts}, Universitext, Springer-Verlag, Berlin, 1998.

\bibitem[Knu81]{Knu81}
Donald~E. Knuth, {\em {T}he art of computer programming: {V}ol. 2:
  {S}eminumerical algorithms}, 2nd ed., Addison-Wesley Publishing Co., Reading,
  Mass., 1981.

\bibitem[Kob84]{Kob84}
N.~Koblitz, {\em $p$-adic {N}umbers, $p$-adic {A}nalysis, and
  {Z}eta-{F}unctions}, 2nd ed., Graduate Texts in Mathematics, vol.~58,
  Springer-Verlag, New York, 1984.

\bibitem[MuPa98]{MuPa98}
D.~Mundici and G.~Panti, {\em The equivalence problem for {B}ratteli diagrams},
  preprint, 1998.

\bibitem[New72]{New72}
M.~Newman, {\em Integral {M}atrices}, Pure and Applied Mathematics, vol.~45,
  Academic Press, New York--London, 1972.

\bibitem[PaTa95]{PaTa95}
Jacob Palis and Floris Takens, {\em Hyperbolicity and sensitive chaotic
  dynamics at homoclinic bifurcations}, Cambridge Studies in Advanced
  Mathematics, vol.~35, Cambridge University Press, 1993.

\bibitem[PaTu82]{PaTu82}
W.~Parry and S.~Tuncel, {\em Classification {P}roblems in {E}rgodic {T}heory},
  London Mathematical Society Lecture Note Series, vol.~67, Statistics:
  Textbooks and Monographs, no.~41, Cambridge University Press, Cambridge--New
  York, 1982.

\bibitem[PaWi77]{PaWi77}
W.~Parry and R.F. Williams, {\em Block coding and a zeta function for finite
  {M}arkov chains}, Proc. London Math. Soc. (3) {\bf 35} (1977), 483--495.

\bibitem[PoZa97]{PoZa97}
M.~Pohst and H.~Zassenhaus, {\em Algorithmic {A}lgebraic {N}umber {T}heory},
  Encyclopedia of Mathematics and its Applications, vol.~30, Cambridge
  University Press, Cambridge, 1997, revised reprint of the 1989 original.

\bibitem[Pru25]{Pru25}
H.~Pr\"ufer, {\em Theorie der {A}belschen {G}ruppen {II}}, Math. Z. {\bf 22}
  (1925), 222--249.

\bibitem[Rad99]{Rad99}
Charles Radin, {\em Miles of tiles}, American Mathematical Society, Providence,
  RI, 1999.

\bibitem[Rot98]{Rot98}
J.J. Rotman, {\em Galois {T}heory}, second ed., Universitext, Springer-Verlag,
  New York, 1998.

\bibitem[Ser77]{Ser77}
J.-P. Serre, {\em Linear {R}epresentations of {F}inite {G}roups}, Graduate
  Texts in Mathematics, vol.~42, Springer-Verlag, New York--Heidelberg, 1977.

\bibitem[Ser79]{Ser79}
J.-P. Serre, {\em Local {F}ields}, Graduate Texts in Mathematics, vol.~67,
  Springer-Verlag, New York--Berlin, 1979.

\bibitem[Ser98]{Ser98}
J.-P. Serre, {\em Abelian $l$-adic {R}epresentations and {E}lliptic {C}urves},
  Research Notes in Mathematics, vol.~7, A K Peters, Ltd., Wellesley, MA, 1998,
  revised reprint of the 1968 original (W.A. Benjamin, Inc.).

\bibitem[SwVo00]{SwVo00}
R.~Swanson and H.~Volkmer, {\em Invariants of weak equivalence in primitive
  matrices}, Ergodic Theory Dynam. Systems {\bf 20} (2000), 611--626.

\bibitem[vdW91]{vdW91}
B.~L. van~der Waerden, {\em Algebra, {V}ol. {II}}, Springer-Verlag, New York,
  1991, Based in part on lectures by E. Artin and E. Noether, Translated from
  the fifth German edition by John R. Schulenberger.

\bibitem[Wag99]{Wag99}
J.B. Wagoner, {\em Strong shift equivalence theory and the shift equivalence
  problem}, Bull. Amer. Math. Soc. (N.S.) {\bf 36} (1999), 271--296.

\bibitem[Wei98]{Wei98}
E.~Weiss, {\em Algebraic {N}umber {T}heory}, Dover, Mineola, NY, 1998.

\end{thebibliography}