Borel quasi-orderings in subsystems of second-order arithmetic
نویسندگان
چکیده
منابع مشابه
Borel Quasi-Orderings in Subsystems of Second-Order Arithmetic
Marcone, A., Bore1 quasi-orderings in subsystems of second-order arithmetic, Annals of Pure and Applied Logic 54 (1991) 265-291. We study the provability in subsystems of second-order arithmetic of two theorems of Harrington and Shelah [6] about Bore1 quasi-orderings of the reals. These theorems turn out to be provable in AT&, thus giving further evidence to the observation that AT&, is the min...
متن کاملSubsystems 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 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 کاملFormalizing Forcing Arguments in Subsystems of Second-Order Arithmetic
We show that certain model-theoretic forcing arguments involving subsystems of second-order arithmetic can be formalized in the base theory, thereby converting them to effective proof-theoretic arguments. We use this method to sharpen conservation theorems of Harrington and Brown-Simpson, giving an effective proof that WKL+0 is conservative over RCA0 with no significant increase in the lengths ...
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: Annals of Pure and Applied Logic
سال: 1991
ISSN: 0168-0072
DOI: 10.1016/0168-0072(91)90050-v