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Page 632 of Mathematical Reviews Vol. , Issue 91B [page]

1991 Mathematical Reviews  
-complete set, and the theories of all constructivizable groups and of groups of recursive automorphisms are recursively isomorphic to arithmetic, ie. are sets of degree 0'@).  ...  Presburger arithmetic (Pr) is the first-order theory of the additive ordered group of integers. If M is a model of Pr and ae M, let t(a) = (2, 173,°°*,Tny***), Where O< r; <i and a=r; (mod i).  ... 

Page 6761 of Mathematical Reviews Vol. , Issue 87m [page]

1987 Mathematical Reviews  
(NZ-VCTR); Kurtz, Stuart A. (1-CHI) Recursion theory and ordered groups. Ann. Pure Appl. Logic 32 (1986), no. 2, 137-151. F.  ...  Recursive orderability of recursive divis- ible groups and “lexicographic” recursive orderability of recursive vector spaces are also studied.  ... 

Page 45 of Mathematical Reviews Vol. 53, Issue 2 [page]

1977 Mathematical Reviews  
The group M, has word, power, and order problems of degree a.  ...  The group M, has solvable word and order problems, and power problem of degree b; M, has solvable word and power problems, and order problem 53 #42663-2668 of degree c.  ... 

Page 1356 of Mathematical Reviews Vol. , Issue 83d [page]

1983 Mathematical Reviews  
MATHEMATICAL LOGIC AND FOUNDATIONS 1356 She shows that all models of the theories of trees in the language «<) and of linear orderings satisfy the recursive embeddability condition. V. K.  ...  He used a recursive total ordering R with field N and type w+ w* for which the set A={n: there are only finitely many R-predecessors of n} is not recursive.  ... 

Page 4609 of Mathematical Reviews Vol. , Issue 2000g [page]

2000 Mathematical Reviews  
4609 03D Computability and recursion theory 2000g:03096 03D20 03F35 De Castro, Rodrigo [de Castro Korgi, Rodrigo} (CL-UNC-MS; Bogota) Recursion in second order bounded arithmetic.  ...  and recursion theory 2000g:03102 els.  ... 

Page 388 of Mathematical Reviews Vol. 56, Issue 2 [page]

1978 Mathematical Reviews  
The author lifts some results concerning strong representability of partial recursive functions and provable recursiveness, proved for ordinary recursion theory [R. W. Ritchie and P. R.  ...  Theorem 8: Let 8 be any strictly r.e. set and let K be any finite partial ordering; then there is a collection of co-recursively enumerable sets, each bi- dense in Q, each Turing equivalent to 8, such  ... 

Page 7 of Mathematical Reviews Vol. 53, Issue 4 [page]

1977 Mathematical Reviews  
It is well-known that the first order theory of ell abelian groups and also the first order theories of several important abelian groups are decidable.  ...  In order to prove this result, the author first gives a recursive  ... 

Page 944 of Mathematical Reviews Vol. , Issue 82c [page]

1982 Mathematical Reviews  
., 1972] showed that second-order arithmetic is interpretable in the first-order theory of certain existentially closed groups.  ...  Some theories of totally ordered abelian groups are studied. Results concerning completeness, elimination of quantifiers and embedding 82c:03052  ... 

Page 2806 of Mathematical Reviews Vol. , Issue 82g [page]

1982 Mathematical Reviews  
This paper describes a new approach to coding second-order arithmetic, and applies it to showing that the first-order theories of many reducibility orderings in recursion theory are recursively isomorphic  ...  This result shows that the notion of creativity is wider than that of completeness in recursion theory.” Horst Reichel (Magdeburg) Gonéaroy, S. S. Autostability of models and abelian groups.  ... 

Eliminating Unbounded Search in Computable Algebra [chapter]

Alexander G. Melnikov
2017 Lecture Notes in Computer Science  
computable structure theory [AK00, EG00].  ...  Klaimullin, Melnikov and Ng [KMNa] have recently suggested a new systematic approach to algorithms in algebra which is intermediate between computationally feasible algebra [CR91, KNRS07] and abstract  ...  Computable structure theory and combinatorial group theory often rely on algorithms that are not even primitive recursive, let alone polynomial-time.  ... 
doi:10.1007/978-3-319-58741-7_8 fatcat:r5gtcd753jgk3cx2hlcmt5sbt4

Page 4645 of Mathematical Reviews Vol. , Issue 80M [page]

1980 Mathematical Reviews  
Gurevié has proved that the lattice theory of abelian lattice- ordered groups is undecidable [Algebra i Logika 6 (1967), 45—62; MR 36 #92], but even an expanded theory of abelian linearly ordered groups  ...  B. 80m:03080 Recursion theory on orderings. I. A model-theoretic setting. J. Symbolic Logic 44 (1979), no. 3, 383-402.  ... 

Page 5415 of Mathematical Reviews Vol. , Issue 87j [page]

1987 Mathematical Reviews  
His approach is to use an analogue of recursive function theory in a group-theoretical setting. Let G be a finitely generated, recursively presented group; let w [resp.  ...  Recursive functions in group theory. Illinois J. Math. 30 (1986), no. 2, 284-294. The author proves several variants on the Boone- Higman theorem [W. W.  ... 

Page 4415 of Mathematical Reviews Vol. , Issue 86j [page]

1986 Mathematical Reviews  
a torsion group T and a field Q = Q with Q[T] # Q[T|.  ...  Let K, K,, K2 be fields of characteristic zero containing all roots of unity, and let G,G,,G2 be abelian groups with G torsion-free, and with the torsion subgroups T;,7T> of Gi,Gz2 of equal order (if finite  ... 

Page 3143 of Mathematical Reviews Vol. , Issue 95f [page]

1995 Mathematical Reviews  
Summary: “Let G be a finite group, We prove that the theory of abelian-by-G groups is decidable if and only if the theory of modules over the group ring Z[G] is decidable: Then we study some model-theoretic  ...  Then there is Z C G(Q) of Haar measure one such that if o € Z, then Q(c) is axiomatized by a first-order theory 7(a), and this 7(c) is open, model-complete and coherent. M.  ... 

Every low Boolean algebra is isomorphic to a recursive one

Rod Downey, Carl G. Jockusch
1994 Proceedings of the American Mathematical Society  
to any recursive structure.  ...  from models of the theory.  ...  It follows that for any countable model L\ of Tdis there is a countable model L2 of T2 such that Dg(L{) = Dg(L2), and vice-versa. Hence T2 and Tdis have the same Turing and lowness ordinals.  ... 
doi:10.1090/s0002-9939-1994-1203984-4 fatcat:3irj3hm7mveebbmhqcfsana4r4
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