Techniques in weak analysis for conservation results

Fernandes, António; Ferreira, Fernando; Ferreira, Gilda

http://hdl.handle.net/10400.2/10484

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Authors

Fernandes, António

Ferreira, Fernando

Ferreira, Gilda

Abstract(s)

We review and describe the main techniques for setting up systems of weak analysis, i.e. formal systems of second-order arithmetic related to subexponential classes of computational complexity. These involve techniques of proof theory (e.g., Herbrand’s theorem and the cut-elimination theorem) and model theoretic techniques like forcing. The techniques are illustrated for the particular case of polytime computability. We also include a brief section where we list the known results in weak analysis.