Finitely axiomatized theories lack self?comprehension

نویسندگان

چکیده

In this paper, we prove that no consistent finitely axiomatized theory one-dimensionally interprets its own extension with predicative comprehension. This constitutes a result the flavor of Second Incompleteness Theorem whose formulation is completely arithmetic-free. Probably most important novel feature distinguishes our from previous results kind it applicable to arbitrary weak theories, rather than extensions some base theory. The methods used in proof main yield new perspective on notion sequential theory, setting forcing-interpretations.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A note on the interpretability logic of finitely axiomatized theories

Ill [6] Albert Visser shows that ILP completely axiomatizes all schemata about provabihty and relative interpretability that are prov-able in finitely axiomatized theories. In this paper we introduce a system called ILP ~ that completely axiomatizes the arithmetically valid principles of provability in and interpretabihty over such theories. To prove the arith-metical completeness of ILP ~ we u...

متن کامل

A Finitely Axiomatized Formalization of Predicate Calculus with Equality

We present a formalization of first-order predicate calculus with equality which, unlike traditional systems with axiom schemata or substitution rules, is finitely axiomatized in the sense that each step in a formal proof admits only finitely many choices. This formalization is primarily based on the inference rule of condensed detachment of C. A. Meredith. The usual primitive notions of free v...

متن کامل

A Finitely Axiomatized Formalization of Predicate Calculus with Equality

We present a formalization of first-order predicate calculus with equality which, unlike traditional systems with axiom schemata or substitution rules, is finitely axiomatized in the sense that each step in a formal proof admits only finitely many choices. This formalization is primarily based on the inference rule of condensed detachment of C. A. Meredith. The usual primitive notions of free v...

متن کامل

A Finitely Axiomatized Formalization of Predicate Calculus with Equality

We present a formalization of first-order predicate calculus with equality which, unlike traditional systems with axiom schemata or substitution rules, is finitely axiomatized in the sense that each step in a formal proof admits only finitely many choices. This formalization is primarily based on the inference rule of condensed detachment of C. A. Meredith. The usual primitive notions of free v...

متن کامل

A Finitely Axiomatized Formalization of Predicate Calculus with Equality

We present a formalization of first-order predicate calculus with equality which, unlike traditional systems with axiom schemata or substitution rules, is finitely axiomatized in the sense that each step in a formal proof admits only finitely many choices. This formalization is primarily based on the inference rule of condensed detachment of C. A. Meredith. The usual primitive notions of free v...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Bulletin of The London Mathematical Society

سال: 2022

ISSN: ['1469-2120', '0024-6093']

DOI: https://doi.org/10.1112/blms.12708