TRANSFINITE RECURSION IN HIGHER REVERSE MATHEMATICS
نویسندگان
چکیده
منابع مشابه
Nonstandard Models in Recursion Theory and Reverse Mathematics
We give a survey of the study of nonstandard models in recursion theory and reverse mathematics. We discuss the key notions and techniques in effective computability in nonstandard models, and their applications to problems concerning combinatorial principles in subsystems of second order arithmetic. Particular attention is given to principles related to Ramsey’s Theorem for Pairs.
متن کاملRanked Structures and Arithmetic Transfinite Recursion
ATR0 is the natural subsystem of second-order arithmetic in which one can develop a decent theory of ordinals. We investigate classes of structures which are in a sense the “well-founded part” of a larger, simpler class, for example, superatomic Boolean algebras (within the class of all Boolean algebras). The other classes we study are: well-founded trees, reduced Abelian p-groups, and countabl...
متن کاملTransfinite recursion and computation in the iterative conception of set
Transfinite recursion is an essential component of set theory. In this paper, we seek intrinsically justified reasons for believing in recursion and the notions of higher computation that surround it. In doing this, we consider several kinds of recursion principles and prove results concerning their relation to one another. We then consider philosophical motivations for these formal principles ...
متن کاملNon-principal Ultrafilters, Program Extraction and Higher Order Reverse Mathematics
We investigate the strength of the existence of a non-principal ultrafilter over fragments of higher order arithmetic. Let (U) be the statement that a non-principal ultrafilter on N exists and let ACA0 be the higher order extension of ACA0. We show that ACA0 + (U) is Π2-conservative over ACA0 and thus that ACA0 +(U) is conservative over PA. Moreover, we provide a program extraction method and s...
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: The Journal of Symbolic Logic
سال: 2015
ISSN: 0022-4812,1943-5886
DOI: 10.1017/jsl.2015.2