Full and hat inductive definitions are equivalent in NBG
نویسندگان
چکیده
منابع مشابه
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 کاملFull 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 ACA 0 , 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 ∆ 1 0-LFP an...
متن کاملForcing for hat inductive definitions in arithmetic
By forcing, we give a direct interpretation of ÎDω into Avigad’s FP. To the best of the author’s knowledge, this is one of the simplest applications of forcing to “real problems”.
متن کاملCyclic and Inductive Calculi are equivalent
Brotherston and Simpson [citation] have formalized and investigated cyclic reasoning, reaching the important conclusion that it is at least as powerful as inductive reasoning (specifically, they showed that each inductive proof can be translated into a cyclic proof). We add to their investigation by proving the converse of this result, namely that each inductive proof can be translated into an ...
متن کاملInductive-Inductive Definitions
We present a principle for introducing new types in type theory which generalises strictly positive indexed inductive data types. In this new principle a set A is defined inductively simultaneously with an A-indexed set B, which is also defined inductively. Compared to indexed inductive definitions, the novelty is that the index set A is generated inductively simultaneously with B. In other wor...
متن کاملذخیره 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: Archive for Mathematical Logic
سال: 2014
ISSN: 0933-5846,1432-0665
DOI: 10.1007/s00153-014-0403-x