Analysis in weak systems

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

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

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Autores

Fernandes, António M.

Ferreira, Fernando

Ferreira, Gilda

Resumo(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.

Palavras-chave

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

URI

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

Citação

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.