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Someone with a J1 Scholar visa becomes a resident alien for tax purposes in the US on Jan 1, 2018 (following the two calendar years' rule). Still, under the saving clause, it may be possible to claim tax treaty benefits for part of 2018. As explained in Publication 519, one should just file 1040, reporting somewhere the exempt part of income under the treaty.

Provided the above is correct, is it still possible to take the now standard 12k $ deduction on the income from the remaining part of 2018?

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Yes, since you are a resident alien for 2018, you can take the $12,000 standard deduction (for Single or Married Filing Separately) after applying the tax treaty.

There is no "remaining part of 2018" -- it is all of 2018 -- you are a resident alien for all of 2018, and that's why you are able to take the standard deduction (dual-status aliens cannot take the standard deduction). This is true even if you are able to use the tax treaty for income from the whole year.

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