  It is well known that there are various models of gravitation: the metrical
Hilbert-Einstein theory, a wide class of intrinsically Lorentz-invariant tetrad
theories (of course, generally-covariant in the space-time sense), and many
gauge models based on various internal symmetry groups (Lorentz, Poincare,
${\rm GL}(n,\mathbb{R})$, ${\rm SU}(2,2)$, ${\rm GL}(4,\mathbb{C})$, and so
on). One believes usually in gauge models and we also do it. Nevertheless, it
is an interesting idea to develop the class of ${\rm
GL}(4,\mathbb{R})$-invariant (or rather ${\rm GL}(n,\mathbb{R})$-invariant)
tetrad ($n$-leg) generally covariant models. This is done below and motivated
by our idea of bringing back to life the Thales of Miletus idea of affine
symmetry. Formally, the obtained scheme is a generally-covariant tetrad
($n$-leg) model, but it turns out that generally-covariant and intrinsically
affinely-invariant models must have a kind of non-accidental Born-Infeld-like
structure. Let us also mention that they, being based on tetrads ($n$-legs),
have many features common with continuous defect theories. It is interesting
that they possess some group-theoretical solutions and more general
spherically-symmetric solutions. It is also interesting that within such
framework the normal-hyperbolic signature of the space-time metric is not
introduced by hand, but appears as a kind of solution, rather integration
constants, of differential equations. Let us mention that our Born-Infeld
scheme is more general than alternative tetrad models. It may be also used
within more general schemes, including also the gauge ones.
