max planck institut
informatik

# MPI-I-98-2-007

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

### Vorobyov, Sergei

MPI-I-98-2-007. April 1998, 36 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
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.
Acknowledgement:
References to related material:

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URL to this document: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1998-2-007
BibTeX
@TECHREPORT{Vorobyov98-2-007,
AUTHOR = {Vorobyov, Sergei},
TITLE = {The most nonelementary theory (a direct lower bound proof)},
TYPE = {Research Report},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},