Below are links to two articles dealing with the claims of Calvinism regarding Acts 13:48. The first is an excerpt from a larger article by Brian Abasciano on Corporate Election. In that article Abasciano briefly tackles the Greek and shows how the Calvinist interpretation is not demanded by the Greek and is contrary to the context. He takes the view that the verb often translated “ordained” is most likely passive and shows why this is not a problem for the Arminian interpretation.
The second link goes to a brief article by Jack Cottrell. He takes the view that the verb should be translated in the middle voice and gives contextual reasons that make better sense of the text than the Calvinist view.
Both views are reasonable and give solid alternatives to the Calvinist view which holds up this passage as a main prooftext for unconditional election.