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

1991
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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). ...##
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Page 6761 of Mathematical Reviews Vol. , Issue 87m
[page]

1987
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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. ...##
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Page 45 of Mathematical Reviews Vol. 53, Issue 2
[page]

1977
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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. ...##
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Page 1356 of Mathematical Reviews Vol. , Issue 83d
[page]

1983
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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*. ...##
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Page 4609 of Mathematical Reviews Vol. , Issue 2000g
[page]

2000
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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. ...##
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Page 388 of Mathematical Reviews Vol. 56, Issue 2
[page]

1978
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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 ...##
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Page 7 of Mathematical Reviews Vol. 53, Issue 4
[page]

1977
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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*...##
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Page 944 of Mathematical Reviews Vol. , Issue 82c
[page]

1982
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Mathematical Reviews
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., 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 ...##
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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*. ...##
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Eliminating Unbounded Search in Computable Algebra
[chapter]

2017
*
Lecture Notes in Computer Science
*

computable structure

doi:10.1007/978-3-319-58741-7_8
fatcat:r5gtcd753jgk3cx2hlcmt5sbt4
*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. ...##
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Page 4645 of Mathematical Reviews Vol. , Issue 80M
[page]

1980
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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. ...##
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Page 5415 of Mathematical Reviews Vol. , Issue 87j
[page]

1987
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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. ...##
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Page 4415 of Mathematical Reviews Vol. , Issue 86j
[page]

1986
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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 ...##
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Page 3143 of Mathematical Reviews Vol. , Issue 95f
[page]

1995
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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. ...##
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Every low Boolean algebra is isomorphic to a recursive one

1994
*
Proceedings of the American Mathematical Society
*

to any

doi:10.1090/s0002-9939-1994-1203984-4
fatcat:3irj3hm7mveebbmhqcfsana4r4
*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. ...
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