MPI-INF/SWS Research Reports 1991-2017

# MPI-I-98-2-007

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

### Vorobyov, Sergei

#### April 1998, 36 pages.

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##### 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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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},