Model-theoretic studies on subsystems of second order arithmetic
نویسندگان
چکیده
منابع مشابه
Subsystems of Second Order Arithmetic Second Edition
Foundations of mathematics is the study of the most basic concepts and logical structure of mathematics, with an eye to the unity of human knowledge. Almost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core...
متن کاملFundamental notions of analysis in subsystems of second-order arithmetic
We develop fundamental aspects of the theory of metric, Hilbert, and Banach spaces in the context of subsystems of second-order arithmetic. In particular, we explore issues having to do with distances, closed subsets and subspaces, closures, bases, norms, and projections. We pay close attention to variations that arise when formalizing definitions and theorems, and study the relationships betwe...
متن کاملA review of Subsystems of Second Order Arithmetic
This is the first book to appear on “reverse mathematics”. The book provides an excellent introduction to the area and is packed with some interesting theorems and uses of mathematical logic. The theme of reverse mathematics is to take a theorem of mathematics and determine the set existence axioms needed to prove the chosen theorem. The goal is to show that the theorem is actually equivalent t...
متن کاملThe Prehistory of the Subsystems of second-order Arithmetic
This paper presents a systematic study of the prehistory of the traditional subsystems of second-order arithmetic that feature prominently in the reverse mathematics program of Friedman and Simpson. We look in particular at: (i) the long arc from Poincaré to Feferman as concerns arithmetic definability and provability, (ii) the interplay between finitism and the formalization of analysis in the...
متن کاملExtensions of Commutative Rings in Subsystems of Second Order Arithmetic
We prove that the existence of the integral closure of a countable commutative ring R in a countable commutative ring S is equivalent to Arithmetical Comprehension (over RCA0). We also show that i) the Lying Over ii) the Going Up theorem for integral extensions of countable commutative rings and iii) the Going Down theorem for integral extensions of countable domains R ⊂ S, with R normal, are p...
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: Tohoku Mathematical Publications
سال: 2000
ISSN: 1343-9499,1880-876X
DOI: 10.2748/tmpub.17.1