Analysis in weak systems

Fernandes, António M.; Ferreira, Fernando; Ferreira, Gilda

http://hdl.handle.net/10400.2/7092

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Authors

Fernandes, António M.

Ferreira, Fernando

Ferreira, Gilda

Abstract(s)

The authors survey and comment their work on weak analysis. They describe the basic set-up of analysis in a feasible second-order theory and consider the impact of adding to it various forms of weak Konig's lemma. A brief discussion of the Baire categoricity theorem follows. It is then considered a strengthening of feasibility obtained (fundamentally) by the addition of a counting axiom and showed how it is possible to develop Riemann integration in the stronger system. The paper finishes with three questions in weak analysis.

Keywords

Mathematical logic Weak analysis Bounded arithmetic Weak Konig's lemma Polytime computability Integration Baire category theorem

URI

http://hdl.handle.net/10400.2/7092

Citation

Fernandes, António M.; Ferreira, Fernando; Ferreira, Gilda - Analysis in weak systems. In Gouveia, Paula [et al.], ed. - "Logic and computation [Em linha]: essays in honour of Amílcar Sernadas". [S.l.]: College Publication, 2017. ISBN 978-1848902480. 21 p.