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This may be well-known or simply deducible from the existing theorems, but I didn't find an answer in my set theory books:

Is there a model of $ZFC$ in which there are no $\kappa$-Souslin trees where $\kappa$ is the first inaccessible cardinal?

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Dear Shahram and Mohammad: I deleted my answer since my answer was simply indicating the result that motivates Shahram's question, namely, in L the first inaccessible carries a Suslin tree. –  Ali Enayat Oct 1 '13 at 9:31
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