Explicit mathematics with monotone inductive definitions: A survey

被引：0

作者：

Rathjen, M ^{[1
]}

机构：

[1] Univ Leeds, Dept Pure Math, Leeds LS2 9JT, W Yorkshire, England

来源：

REFLECTIONS ON THE FOUNDATIONS OF MATHEMATICS: ESSAYS IN HONOR OF SOLOMON FEFERMAN | 2002年 / 15卷

关键词：

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper provides a survey of results about the strength of Feferman's theory of explicit mathematics augmented by least fixed point principles for monotone inductive definitions. The paper gathers all the results that are known up till now and also proves a heretofore unpublished result concerning an upper bound for the strength of T-0 + MID.

引用

页码：329 / 346

页数：18

共 50 条

[21] On the complexity of inductive definitions
Cenzer, Douglas
Remmel, Jeffrey B.
[J]. MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE, 2006, 16 (05) : 763 - 788
[22] ANALYTIC INDUCTIVE DEFINITIONS
CENZER, D
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (03): : A376 - A376
[23] Transforming inductive definitions
Proietti, M
Pettorossi, A
[J]. LOGIC PROGRAMMING: PROCEEDINGS OF THE 1999 INTERNATIONAL CONFERENCE ON LOGIC PROGRAMMING, 1999, : 486 - 499
[24] Topological inductive definitions
Curi, Giovanni
[J]. ANNALS OF PURE AND APPLIED LOGIC, 2012, 163 (11) : 1471 - 1483
[25] PARTIAL INDUCTIVE DEFINITIONS
HALLNAS, L
[J]. THEORETICAL COMPUTER SCIENCE, 1991, 87 (01) : 115 - 142
[26] ANALYTIC INDUCTIVE DEFINITIONS
CENZER, D
[J]. JOURNAL OF SYMBOLIC LOGIC, 1974, 39 (02) : 310 - 312
[27] INDUCTIVE DEFINITIONS AND COMPUTABILITY
GRILLIOT, TJ
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 158 (02) : 309 - &
[28] ABSTRACT INDUCTIVE AND CO-INDUCTIVE DEFINITIONS
Curi, Giovanni
[J]. JOURNAL OF SYMBOLIC LOGIC, 2018, 83 (02) : 598 - 616
[29] COMPLEXITY OF EXPLICIT DEFINITIONS
FRIEDMAN, H
[J]. ADVANCES IN MATHEMATICS, 1976, 20 (01) : 18 - 29
[30] FUNCTIONAL INTERPRETATION AND INDUCTIVE DEFINITIONS
Avigad, Jeremy
Towsner, Henry
[J]. JOURNAL OF SYMBOLIC LOGIC, 2009, 74 (04) : 1100 - 1120

← 1 2 3 4 5 →