PHYSICAL REVIEW D, cilt.81, sa.10, 2010 (SCI-Expanded)
We define various Born-Infeld gravity theories in 3 + 1 dimensions which reduce to Horava's model at the quadratic level in small curvature expansion. In their exact forms, our actions provide z -> infinity extensions of Horava's gravity, but when small curvature expansion is used, they reproduce finite z models, including some half-integer ones.