(abridged) We present B,V,I CCD photometry of about 40000 stars in four regions of the Fornax dSph. Using the resultant CMDs, many already known age-tracers are investigated, and new CMD features are also detected: we show that blue HB stars may be present in the outer regions, and measure the luminosity of the AGB bump. We measure a corrected distance modulus (m-M)o = 20.70+/-0.12, based on the RGB tip luminosity, which is in good agreement with that obtained from the mean magnitude of old HB stars [(m-M)o=20.76+/-0.04] and with previous results. The (B-I) distribution of the RG stars can be approximately described as the superposition of two populations. The dominant component, comprising ~70% of the red giant stars, consists of relatively metal-enriched intermediate-age stars, whose mean metallicity is [Fe/H]=-1.39+/-0.15 (the age-corrected metallicity would be [Fe/H] ~ -1.0+/-0.15). The dominant intermediate-age component has an intrinsic color dispersion sigma(B-I)=0.06+/-0.01mag, corresponding to a relatively low abundance dispersion, sigma[Fe/H]=0.12+/-0.02dex. In addition, there is a small population of giants on the blue side of the RGB, whose spatial distribution is consistent with that of old horizontal branch stars, and completely different from that of the younger population. This unambiguously qualifies them as old and metal-poor. The exceptional color width of the Fornax RGB is therefore due to the presence of two main populations, yielding a large abundance range (-2.0<[Fe/H]<-0.7). This evidence suggests a scenario in which this galaxy started forming a stellar halo and its surrounding clusters together about 10-13 Gyr ago, then a major SF episode occurred after several Gyr.
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