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>>10447988>>10448133Now the field not presented :
-proof theory : all historical books about intuitionistic logic and linear logic :J-Y Girard, Barendregt lambda calculus (2 books : -syntax and semantics, and -with types) Then you can go on to see homotopy type theory (I advise you to read 3 courses on : category theory (Mc Lane), then homological algebra, then homotopy theory (I used the top tier french school ref but it's all in french, though the bible are translated : EGA...) to have a solid background for the rest of the subject :
-Jacob Lurie for algebraic set and topos theory
-Jacobs book : categorical logic and type theory
-check for topos theory by yourself and seek the big names like Hylands
-check Shelah's paper and from there go find the related course's note . In model theory this guy did everything so you'll always find what you want.
-For model theory in algebra and number theory: Chatzidakis, Bouscaren, Pierre Simon (those are the one I know personally but you can check this page and the lecture notes related)
http://modvac18.math.ens.fr/Finally, I'm quite weak on game theory, languages and omega-logic but juste take a course on finite automata and from there take the big names and go check their books inductively you'll get to an advanced level. (on a side note infinitary games are related to analytic hierarchy in descriptive set theory (and the real determination is a related problem) so you can go back to this area through this one.
So yes, this picture is at the very least, lacking.
