We explore models of intersecting brane-worlds with induced gravity terms on\udcodimension one branes and on their intersection. Maximally symmetric solutions\udfor the branes and the intersection are found. We find new self-accelerating\udsolutions. In a 6d spacetime, the solutions realize the see-saw modification of\udgravity where the UV scale of the modification to 4d gravity is determined by\ud6d Planck scale given by $M_6 \sim 10^-3$eV and the IR scale of the\udmodification is determined by $M_6^2/M_4 \sim H_0 \sim 10^-42$ GeV where\ud$H_0$ is present-day Hubble scale. We find that it is increasingly difficult to\udconstruct phenomenologically viable models in higher-dimensional spacetime due\udto the necessity to have the lower value for the fundamental Planck scale to\udrealize the late time acceleration. It is found that the system also admits\udself-tuning solutions where the tension at the intersection does not change the\udgeometry of the intersection. The induced gravity terms can avoid the necessity\udto compactify the extra dimensions. Finally, we discuss the possibility to have\udordinary matter at the intersection, without introducing any regularisation,\udusing the induced gravity terms.
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