منابع مشابه
Descriptive inner model theory
The purpose of this paper is to outline some recent progress in descriptive inner model theory, a branch of set theory which studies descriptive set theoretic and inner model theoretic objects using tools from both areas. There are several interlaced problems that lie on the border of these two areas of set theory, but one that has been rather central for almost two decades is the conjecture kn...
متن کاملTranslation procedures in descriptive inner model theory∗†
We develop a basic translation procedure that translates a hod mouse to an equivalent mouse. Unlike the translation procedure used by Steel and Zhu, our procedure works in a coarse setting without assuming AD+. Nevertheless, the procedure resembles the one developed by Steel in [8]. We use the translation procedures to answer a question of Trevor Wilson. Namely, we show that if there is a stati...
متن کاملDeconstructing Inner Model Theory
In this paper we shall repair some errors and fill some gaps in the inner model theory of [2]. The problems we shall address affect some quite basic definitions and proofs. We shall be concerned with condensation properties of canonical inner models constructed from coherent sequences ~ E of extenders as in [2]. Condensation results have the general form: if x is definable in a certain way over...
متن کاملDescriptive set theory and uncountable model theory
In the early days of the development of model theory it was considered natural and was certainly beneficial to assume that the theories under investigation were in a countable language. The primary advantage of this assumption was the presence of the Omitting Types Theorem of Grzegorczyk, Mostowski, and Ryll-Nardzewski [1], which generalized arguments of Henkin [3] and Orey [8]. Following this,...
متن کاملDescriptive Inner Model Theory , Large Cardinals , and Combinatorics Research Statement Nam Trang
My research interest is in mathematical logic and set theory. My current research focuses on studying the connections between inner models, (determined) sets of reals, hybrid structures (such as HOD1 of determinacy models), forcing, and strong combinatorial principles (such as the Proper Forcing Axiom (PFA), (generalizations of) the tree property, the Unique Branch Hypothesis (UBH)). I’m also i...
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 Bulletin of Symbolic Logic
سال: 2013
ISSN: 1079-8986,1943-5894
DOI: 10.2178/bsl.1901010