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The most nonelementary theory (a direct lower bound proof)

Vorobyov, Sergei

April 1998, 36 pages.

Status: available - back from printing

We give a direct proof by generic reduction that a decidable rudimentary theory of finite typed sets [Henkin 63, Meyer 74, Statman 79, Mairson 92] requires space exceeding infinitely often an exponentially growing stack of twos. This gives the highest currently known lower bound for a decidable logical theory and affirmatively answers to Problem 10.13 of [Compton & Henson 90]: Is there a `natural' decidable theory with a lower bound of the form $\exp_\infty(f(n))$, where $f$ is not linearly bounded? The highest previously known lower and upper bounds for `natural' decidable theories, like WS1S, S2S, are `just' linearly growing stacks of twos.

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  AUTHOR = {Vorobyov, Sergei},
  TITLE = {The most nonelementary theory (a direct lower bound proof)},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-98-2-007},
  MONTH = {April},
  YEAR = {1998},
  ISSN = {0946-011X},