Connections between descriptive set theory and HF-logic

• Main Author: Romanovski, Iakov.
• Other Authors: Makkai, M. (advisor)
• Format: Others
• Language: en
• Published: McGill University 1997
• Subjects: Mathematics.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=27901

In this thesis we give a positive answer to the question "Is it true that the set of all definable elements of $ rm { bf R sp{f}} subset$ R, where R is the set of real numbers, is elementary substructure of R in HF-logics?" This result is proved under the set-theoretic hypothesis of Projective Determinacy (PD). We also study the structure of hereditary finite closure of a set; the notions of pattern and matching of patterns are discussed in sufficient detail.