Applicative theories for the polynomial hierarchy of time and its levels☆
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Work partially supported by the ESF research project Dialogical Foundations of Semantics within the ESF Eurocores program LogICCC, LogICCC/0001/2007 (funded by the Portuguese Science Foundation, FCT). The first author was also supported by the project Hilbertʼs Legacy in the Philosophy of Mathematics, PTDC/FIL-FCI/109991/2009 from FCT. The second author was also supported by the Fundação para a Ciência e a Tecnologia through the project Functional interpretations of arithmetic and analysis, PTDC/MAT/104716/2008, and PEst OE/MAT/UI0209/2011. This paper is a revised and enlarged—in particular, by the treatment of the levels of the polynomial hierarchy—version of the conference paper [14]. We thank Thomas Strahm and the anonymous referees for valuable comments.