Suppose one is starting their math PhD in the US and is considering doing research in logic. Let's roughly split "logic" into "pure logic" and "applied logic".
How hard will it be for them to get academic positions to a math PhD with specialization in logic (given that they don't come from a top logic department, like Berkeley, or even Wisconsin; but from a group I university). Would it be easier if they have a PhD in pure or applied logic? In the latter case, how possible is it to work in two areas? (E.g. if one does applied logic related to computer science/natural language, is it possible to eventually become a professor in both math and computer science/linguistics?)
(I understand that many answers will say that it depends on the research that the PhD did/adviser/connections, etc., but let's just assume that the research if fine (not exceptional), the adviser is a more or less known logician. I just wanted to estimate how hard it is to get academic jobs for a logic person compared to pure mathematicians, as well as if it's possible to work in two areas if one specializes in applied logic.)