A Theory of Explicit Mathematics Equivalent to ID1

نویسندگان

  • Reinhard Kahle
  • Thomas Studer
چکیده

We show that the addition of name induction to the theory EETJ + (LEM-IN) of explicit elementary types with join yields a theory proof-theoretically equivalent to ID1.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Theory of Explicit Mathematics Equivalent to Id 1 a Theory of Explicit Mathematics Equivalent to Id 1

We show that the addition of name induction to the theory EETJ + (LEM-IN) of explicit elementary types with join yields a theory proof-theoretically equivalent to ID1.

متن کامل

The proof-theoretic analysis of transfinitely iterated quasi least fixed points

The starting point of this article is an old question asked by Feferman in his paper on Hancock’s conjecture [6] about the strength of ID1. This theory is obtained from the well-known theory ID1 by restricting fixed point induction to formulas that contain fixed point constants only positively. The techniques used to perform the proof-theoretic analysis of ID1 also permit to analyze its transfi...

متن کامل

A History of Selected Topics in Categorical Algebra I: From Galois Theory to Abstract Commutators and Internal Groupoids

This paper is a chronological survey, with no proofs, of a direction in categorical algebra, which is based on categorical Galois theory and involves generalized central extensions, commutators, and internal groupoids in Barr exact Mal’tsev and more general categories. Galois theory proposes a notion of central extension, and motivates the study of internal groupoids, which is then used as an a...

متن کامل

Duals of Some Constructed $*$-Frames by Equivalent $*$-Frames

Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. W...

متن کامل

Full and Hat Inductive Definitions Are Equivalent in NBG

A new research project has, quite recently, been launched to clarify how different, from systems in second order number theory extending ACA0, those in second order set theory extending NBG (as well as those in n+3-th order number theory extending the so-called Bernays Gödel expansion of full n+2-order number theory etc.) are. In this article, we establish the equivalence between ∆0-LFP and ∆ 1...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2000