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In  John Burgess describes predicative versions of Frege's logic and poses the problem of finding their exact arithmetical strength. I prove here that PV, the simplest such theory, is equivalent… Continue Reading
Relations between some theories of semigroups (also known as theories of strings or theories of concatenation) and arithmetic are surveyed. In particular Robinson's arithmetic Q is shown to be… Continue Reading
The paper has been realized within the research contract nr.7037/10.05.2011 (RTT-5). Program MANUNET
Determining the computational requirements of formal reasoning is a key task in implementing David Hilbert's foundational program. This paper presents a number of results on the syntactical… Continue Reading
Robinson’s arithmetic Q is given a simple interpretation in Hajek’s weaker relational version Q H that does not use Solovay’s technique of shortening cuts. The result is placed within two research… Continue Reading