Recursion theory and ordered groups
نویسندگان
چکیده
منابع مشابه
Proof theory for lattice-ordered groups
Proof theory can provide useful tools for tackling problems in algebra. In particular, Gentzen systems admitting cut-elimination have been used to establish decidability, complexity, amalgamation, admissibility, and generation results for varieties of residuated lattices corresponding to substructural logics. However, for classes of algebras bearing some family resemblance to groups, such as la...
متن کاملOrdered Groups with Greatest Common Divisors Theory
An embedding (called a GCD theory) of partly ordered abelian group G into abelian l-group Γ is investigated such that any element of Γ is an infimum of a subset (possible non-finite) from G. It is proved that a GCD theory need not be unique. A complete GCD theory is introduced and it is proved that G admits a complete GCD theory if and only if it admits a GCD theory G Γ such that Γ is an Archim...
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In the second half of the class, we will explore limits on computation. These are questions of the form “What types of things can be computed at all?” “What types of things can be computed efficiently?” “How fast can problem XYZ be solved?” We already saw some positive examples in class: problems we could solve, and solve efficiently. For instance, we saw that we can sort n numbers in time O(n ...
متن کاملRecursion Theory and Symbolic Dynamics
A set P ⊆ {0,1}N may be viewed as a mass problem, i.e., a decision problem with more than one solution. By definition, the solutions of P are the elements of P . A mass problem is said to be solvable if at least one of its solutions is recursive. A mass problem P is said to be Muchnik reducible to a mass problem Q if for each solution of Q there exists a solution of P which is Turing reducible ...
متن کاملKleene Automata and Recursion Theory
Following the introduction of a theoretical computational model on innnite objects, the !-input Turing machine, we present a new type of innnite automata, the Kleene automata. We show it recognizes exactly the class of arithmetical !-languages. Essentially, it is a propositional automaton for which the transition relation is recursive and the interpretation of atomic formulas associated with ea...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1986
ISSN: 0168-0072
DOI: 10.1016/0168-0072(86)90049-7