  Using asteroseismic data and stellar evolution models we make the first
detection of a convective core in a Kepler field main-sequence star, putting a
stringent constraint on the total size of the mixed zone and showing that extra
mixing beyond the formal convective boundary exists. In a slightly less massive
target the presence of a convective core cannot be conclusively discarded, and
thus its remaining main-sequence life time is uncertain. Our results reveal
that best-fit models found solely by matching individual frequencies of
oscillations corrected for surface effects do not always properly reproduce
frequency combinations. Moreover, slightly different criteria to define what
the best-fit model is can lead to solutions with similar global properties but
very different interior structures. We argue that the use of frequency ratios
is a more reliable way to obtain accurate stellar parameters, and show that our
analysis 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 with
those obtained from global oscillation properties, and discuss the possible
sources of uncertainties in asteroseismic stellar modeling where further
studies are still needed.
