Premium
Automorphisms of the Lattice of Recursively Enumerable Vector Spaces
Author(s) -
Kalantari Iraj
Publication year - 1979
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19790252502
Subject(s) - recursively enumerable language , automorphism , computer science , citation , lattice (music) , combinatorics , discrete mathematics , information retrieval , theoretical computer science , mathematics , algorithm , world wide web , physics , acoustics
Recursively enumerable (r.e,) algebraic structures have received attention because of their recursion theoretic depth and richness. Although the development of such theories is somewhat analoguous to the development of the theory of r.e. sets, the former is not reducible to or a corollary of the latter. I n fact, on more than one occasion the development of such theories has increased our insight into the theory of r.e. sets. The initial works in this area are due to FROHLICH and SHEPHERDSON [6] and Rasm [14]. The more recent works on vector space structure are due to DEKKER [4, 51, CROSSLEY and NERODE [3], METAKIDES and NERODE [13], REMMEL [El , RETZLAFF [19], and the author [8]. An excellent motivational reference is METAKIDES and NERODE [El. I n this paper we confine ourselves with vector space structure and study the lattice of r.e. vector spaces and ith automorphisms. Let V , denote a countably infinite dimensional, f d y effwtive vector space over a countable recursive field 3. By fully effective we mean that 8, under a fixed Godel numbering has the following properties : 0) operations of vector addition and scalar multiplication on V, are presented by partial recursive functions on the Godel numbers of 8,. (ii) V , has a depedence algorithm, i.e., there is a uniform effective procedure which applied to any TL vectors of V , determines whether or not they are linearly independent.