[Event at CIG] LUW October 6 : being provable in Peano Arithmetic with at most k steps

[jean-yves beziau]

This coming Wednesday, October 6, at 4 pm CET,  one more session of the
Logica Universalis Webinar (LUW).
See details below. Everybody is welcome to join !
Register in advance here:
https://www.springer.com/journal/11787/updates/18988758
Jean-Yves Beziau
Organizer of LUW and President of LUA
http://www.logica-universalis.org/LUAD
>------------------------------------------------------------------------------------------------------------------------------------------------------------
Paulo Guilherme Santos & Reinhard Kahle
NOVA School of Science and Technology, Caparica, Portugal and  University
of Tübingen, Germany
"k-Provability in PA"
Logica Universalis, On-line first June 09, 2021
https://link.springer.com/article/10.1007/s11787-021-00278-1

We study the decidability of k-provability in PA—the relation ‘being
provable in PA with at most k steps’—and the decidability of the
proof-skeleton problem—the problem of deciding if a given formula has a
proof that has a given skeleton (the list of axioms and rules that were
used). The decidability of k-provability for the usual Hilbert-style
formalisation of PA is still an open problem, but it is known that the
proof-skeleton problem is undecidable for that theory. Using new methods,
we present a characterisation of some numbers k for which k-provability is
decidable, and we present a characterisation of some proof-skeletons for
which one can decide whether a formula has a proof whose skeleton is the
considered one. These characterisations are natural and parameterised by
unification algorithms.