What are the current open problems and trends in pure logic research?

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what are the current open problems in logic? in model theory, proof theory and philosophical logic? and what are the trends in research? what do researchers pay more attention to?


p.s
is there any book which gives an outline on the open problems in logic?
 
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Call me a crazy, pie in the sky thinker. But. Since there are approximately 4 people here who are research mathematicians that I can think of, none of whom are logicians, here really isn't a very good place to look. However, since most every mathematician these days has a web page listing their research interests, why not look through a few of those? Pillay has moved to Leeds, Shelah is a brilliant mathematician, just have a look around you.