Rosser’s undecidability theorem for very weak (fuzzy) arithmetics

0510722 - ÚI 2020 RO eng A - Abstract
Badia, G. - Cintula, Petr - Tedder, Andrew
Rosser’s undecidability theorem for very weak (fuzzy) arithmetics.
ManyVal 2019. Book of Abstracts. Bucharest: University of Bucharest, 2019. s. 25-27.
[ManyVal 2019: The International Workshop on Many-Valued Logic /8./. 01.11.2019-03.11.2019, Bucharest]
Institutional support: RVO:67985807

In [7, Theorem III], Rosser famously established that Peano Arithmetic was essentially undecidable, that is, that no consistent extension of it was decidable. After Rosser’s essential undecidability theorem, it was natural to ask for weaker theories of arithmetic that would still yield undecidability along similar lines. Three well known examples of such theories important for us are • Robinson arithmetics Q introduced in [6]. • Grzegorczyk’s arithmetics Q− , introduced in [1], where addition and multiplication are neither total nor functional. • Arithmetics R, also due to Robinson [9, p. 53], which contains only the minimal arithmetical facts which seem to be needed for the proof.
Permanent Link: http://hdl.handle.net/11104/0301117