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Using asteroseismic data and stellar evolution models we make the firstdetection of a convective core in a Kepler field main-sequence star, putting astringent constraint on the total size of the mixed zone and showing that extramixing beyond the formal convective boundary exists. In a slightly less massivetarget the presence of a convective core cannot be conclusively discarded, andthus its remaining main-sequence life time is uncertain. Our results revealthat best-fit models found solely by matching individual frequencies ofoscillations corrected for surface effects do not always properly reproducefrequency combinations. Moreover, slightly different criteria to define whatthe best-fit model is can lead to solutions with similar global properties butvery different interior structures. We argue that the use of frequency ratiosis a more reliable way to obtain accurate stellar parameters, and show that ouranalysis in field main-sequence stars can yield an overall precision of 1.5%,4%, and 10% in radius, mass and age, respectively. We compare our results withthose obtained from global oscillation properties, and discuss the possiblesources of uncertainties in asteroseismic stellar modeling where furtherstudies are still needed.

Stellar ages and convective cores in field main-sequence stars: first asteroseismic application to two Kepler targets