The spectrum of Π31-soundness

Author:

Aguilera J. P.12ORCID,Pakhomov F.23

Affiliation:

1. Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstrasse 8–10, 1040 Vienna, Austria

2. Department of Mathematics, University of Ghent, Krijgslaan 281-S8, B9000 Ghent, Belgium

3. Steklov Mathematical Institute of the Russian Academy of Sciences, Ulitsa Gubkina 8, Moscow 117966, Russia

Abstract

We study the Π 3 1 -soundness spectra of theories. Given a recursively enumerable extension T of A C A 0 , O 3 1 ( T ) is defined as the set of all 2-ptykes on which T is correct about well foundedness. This is a measure of how close T is to being Π 3 1 -sound. We carry out a proof-theoretic classification of theories according to O 3 1 ( T ) , as well as a characterization of the sets of the form O 3 1 ( T ) Δ 1 0 . Many of the results generalize to n greater than 3. This article is part of the theme issue ‘Modern perspectives in Proof Theory’.

Funder

Austrian Academy of Sciences

Fonds Wetenschappelijk Onderzoek

Austrian Science Fund

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Reference7 articles.

1. Aguilera JP Pakhomov F. The Π21-consequences of a theory. In press. J. Lond. Math. Soc.

2. Π12-logic, Part 1: Dilators

3. Eléments de logique Π¹_{𝑛}

4. Girard J-Y. 1982 Proof theory and logical complexity, II. Book Draft.

5. Pakhomov FN Walsh J. Reducing ω-model reflection to iterated syntactic reflection. In press. J. Math. Log.

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Modern perspectives in Proof Theory;Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences;2023-04-10

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