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Page 605 of Mathematical Reviews Vol. , Issue 87b [page]

1987 Mathematical Reviews  
The author studies the groups of recursive automorphisms of con- structive Boolean algebras.  ...  605 03D Recursion theory In the first section the author discusses in general the meaning of the major subsets inside the lattice of recursively enumerable sets, and the automorphism and isomorphism problems  ... 

Page 1794 of Mathematical Reviews Vol. , Issue 85e [page]

1985 Mathematical Reviews  
Guichard, David R. (1-VSSR) 85e:03104 Automorphisms of substructure lattices in recursive algebra. Ann. Pure Appl. Logic 25 (1983), no. 1, 47-58.  ...  Let B,. be the free recursive Boolean algebra on countably many generators and let L(B,,.) be the lattice of recursively enu- merable subalgebras of B,..  ... 

Some undecidability results for lattices in recursion theory

Jeffrey Carroll
1986 Pacific Journal of Mathematics  
Recursive Boolean algebras have been more widely examined and, in the second section, for any infinite recursive Boolean algebra, the lattice of its r.e. subalgebras is shown to be undedicable.  ...  The lattice has not been examined as closely as the r.e. substructure lattices of other recursive objects such as vector spaces, Boolean algebras, and fields ([NRl] provides a comprehensive survey of this  ...  Please do not use built up fractions in the text of the manuscript. However, you may use them in the displayed equations. Underline Greek letters in red, German in green, and script in blue.  ... 
doi:10.2140/pjm.1986.122.319 fatcat:nhhb3yhvyjdfpmm5b4rq2h2iu4

Page 3428 of Mathematical Reviews Vol. , Issue 87g [page]

1987 Mathematical Reviews  
Let v be a constructivization of a structure M. Then M is said to be v-effectively homogeneous if every finite elementary map- ping in M can be extended to a v-recursive automorphism of M.  ...  Moreover |Aut M| = 2®°, but for any constructivization v of M there is no v-recursive automorphism of M except the identity mapping. O. V.  ... 

Abstract dependence, recursion theory, and the lattice of recursively enumerable filters

R.G. Downey
1983 Bulletin of the Australian Mathematical Society  
Both sections are devoted to the study of effectiveness in algebra, realized as analyses of substructures of recursive structures.  ...  DEPENDENCE, RECURSION THEORY, AND THE LATTICE OF RECURSIVELY ENUMERABLE FILTERS R.G. DOWNEY This thesis is divided into two sections.  ...  Department of Mathematics, National University of Singapore, Kent Ri dge 05 11, Singapore.  ... 
doi:10.1017/s0004972700025958 fatcat:jd62dcgn7fdtpk33jdbcz5yjiu

Page 4582 of Mathematical Reviews Vol. , Issue 82k [page]

1982 Mathematical Reviews  
The results fall into three main areas—first-order theories, definability, and automorphisms. The flavor of the results is that “sufficiently closed” substructures of the degrees have a first-order  ...  Let E be the lattice of recursively enumerable sets and let m be a relation in E such that A=, B if and only if (A\ B)U(B~ A) is finite or immune. The author proves the following two theorems.  ... 

Master Index To Volumes 11-3011Volumes 11-23 were published under the former name of "Annals of Mathematical Logic"

1986 Annals of Pure and Applied Logic  
., Automorphisms of the lattice of recursively enumerable sets.  ...  Mills, G., Substructure lattices of models of arithmetic Mitchell, W.J., see Jech, T.  ... 
doi:10.1016/0168-0072(86)90026-6 fatcat:lvxcgirz7zcp7if573hj6t7poi

Local Initial Segments of The Turing Degrees

Bjørn Kjos-Hanssen
2003 Bulletin of Symbolic Logic  
AbstractRecent results on initial segments of the Turing degrees are presented, and some conjectures about initial segments that have implications for the existence of nontrivial automorphisms of the Turing  ...  is the congruence lattice of an algebra (for definitions and properties of congruence lattices see [3] ), a fundamental concept of universal algebra.  ...  Grätzer and Schmidt [4] characterized congruence lattices of algebras.  ... 
doi:10.2178/bsl/1046288724 fatcat:rrfet36v4ngvrjsrkwv3r4i3le

Page 23 of Mathematical Reviews Vol. , Issue 98A [page]

1998 Mathematical Reviews  
We also prove that the standard system of a countable arithmetically saturated model of PA is determined by the lattice of its elementary substructures.”  ...  We consider questions concerning the automorphism group of a countable recursively saturated model of PA.  ... 

Page 6762 of Mathematical Reviews Vol. , Issue 87m [page]

1987 Mathematical Reviews  
Supermaximal substructures were later found to occur in more general settings, such as the lattice of r.e. algebraically closed subfields of a recursively presented field having infinite tran- scendence  ...  In particular, we search for properties of bases which reflect different aspects of the lattice of r.e. substructures of a supermaximal structure.  ... 

Page 4231 of Mathematical Reviews Vol. , Issue 89H [page]

1989 Mathematical Reviews  
It is proved that the property of being a special set is not invariant under automorphisms of the lattice of recursively enumerable sets, and every recursively enumerable Turing degree a > 0 contains a  ...  The generator problem (GP) asks whether there is an algorithm which—given E and a set of terms { g; ---, g,,¢}—-will determine whether e is a member of the substructure generated by g;,---, 2, in any member  ... 

Page 5341 of Mathematical Reviews Vol. , Issue 92j [page]

1992 Mathematical Reviews  
(NZ-VCTR); Stob, M. (1-CLVN) Automorphisms of the lattice of recursively enumerable sets: promptly simple sets. Trans. Amer. Math. Soc. 332 (1992), no. 2, 555-570.  ...  The authors investigate notions of recursion over algebraic struc- tures, continuing a paper by Friedman [in Logic Colloquium 69 (Manchester, 1969), 361-389, North-Holland, Amsterdam, 1971; MR 46 #3275  ... 

Page 2443 of Mathematical Reviews Vol. , Issue 89E [page]

1989 Mathematical Reviews  
(and the cardinality of M). # is said to be finitely partitioned (by the partition M,,---,M, of M) if arbitrary permutations of the M,, M2, --- combine to form an automorphism of #.  ...  Moreover, it is proved that for each nontrivial lattice identity there exist 2” logics from [K, LJ] in each of which that identity is re- jected. V. V.  ... 

Page 2272 of Mathematical Reviews Vol. , Issue 87e [page]

1987 Mathematical Reviews  
A. (2-KAZA) Systems of algorithmic algebras preserving ideals in the lattice of recursively enumerable sets. (Russian. English summary) Kibernetika (Kiev) 1985, no. 5, iv, 123-125, 136.  ...  Some conditions are given for a subsystem of algebras to be maxi- mal in the system of algorithmic algebras of partial recursive func- tions and predicates. G. N.  ... 

Page 750 of Mathematical Reviews Vol. 55, Issue 3 [page]

1978 Mathematical Reviews  
In particular, the author proves that the property of being a degree of solvability is lattice-theoretic. This answers a question stated in H.  ...  Certain properties of the Medvedev lattice. (Russian) Mat. Sb. (N.S.) 101(143) (1976), no. 3, 360-379, 455. The author studies the Medvedev lattice of degrees of difficulty.  ... 
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