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#### The most nonelementary theory (a direct lower bound proof)

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##### Fulltext (public)

1998-2-007

(Any fulltext), 10KB

##### Supplementary Material (public)

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##### Citation

Vorobyov, S.(1998). *The most nonelementary theory (a direct
lower bound proof)* (MPI-I-1998-2-007). Saarbrücken: Max-Planck-Institut für Informatik.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-7A8A-2

##### Abstract

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.