18.11 Wykład dr. Fiodora Pachomowa (Uniwersytet Gandawski, Instytut Stiekłowa w Moskwie)

Serdecznie zapraszamy do wzięcia udziału w wykładzie dr. Fiodora Pachomowa pt.

„Two recent results around Gödel’s Second Incompleteness Theorem.”

Wykład odbędzie się w czwartek, 18.11.2021 w auli im. Marii Ossowskiej (103) (Wydział Filozofii, Krakowskie Przedmieście 3) o godz. 16.45.

ABSTRAKT:
In this talk I will present two recent results: first is due to me [1] and the second is due to Albert Visser and me [2]. The first result is an example of a weak natural theory that proves arithmetization of its own consistency. The second result is a general theorem with the flavor of Second Incompleteness Theorem that is applicable to arbitrary weak first-order theories rather than to extension of some base system. Namely the theorem states that no finitely axiomatizable first order theory one-dimensionally interprets its own extension by predicative comprehension.

[1] Fedor Pakhomov. A weak set theory that proves its own consistency. Preprint, arXiv:1907.00877, 2019, https://arxiv.org/abs/1907.00877
[2] Fedor Pakhomov and Albert Visser. Finitely axiomatized theories lack self-comprehension. Preprint, arXiv:2109.02548, 2021, https://arxiv.org/abs/2109.02548