Systems of Explicit Mathematics with Non-Constructive µ-Operator, Part II
نویسندگان
چکیده
This paper is mainly concerned with proof-theoretic analysis of some second-order systems of explicit mathematics with a non-constructive minimum operator. By introducing axioms for variable types we extend our first-order theory BON to the elementary explicit type theory EET and add several forms of induction as well as axioms for ,u. The principal results then state: EET(p) plus set induction [type induction, formula induction) is proof-theoretically equivalent to Peano arithmetic PA (the second-order system (@,-CA) .
منابع مشابه
Applicative Theories and Explicit Mathematics
[5] Solomon Feferman and Gerhard Jäger. Systems of explicit mathematics with non-constructive µ-operator. [6] Solomon Feferman and Gerhard Jäger. Systems of explicit mathematics with non-constructive µ-operator. [9] Susumu Hayashi and Satoshi Kobayashi. A new formulation of Feferman's system of functions and classes and its relation to Frege structures.
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ورودعنوان ژورنال:
- Ann. Pure Appl. Logic
دوره 79 شماره
صفحات -
تاریخ انتشار 1996