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

1987
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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 ...##
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Page 1794 of Mathematical Reviews Vol. , Issue 85e
[page]

1985
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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,.. ...##
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Some undecidability results for lattices in recursion theory

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. ...

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

1983
*
Bulletin of the Australian Mathematical Society
*

Both sections are devoted to the study

doi:10.1017/s0004972700025958
fatcat:jd62dcgn7fdtpk33jdbcz5yjiu
*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. ...##
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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. ...##
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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
*

.,

doi:10.1016/0168-0072(86)90026-6
fatcat:lvxcgirz7zcp7if573hj6t7poi
*Automorphisms**of*the*lattice**of**recursively*enumerable sets. ... Mills, G.,*Substructure**lattices**of*models*of*arithmetic Mitchell, W.J., see Jech, T. ...##
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Local Initial Segments of The Turing Degrees

2003
*
Bulletin of Symbolic Logic
*

AbstractRecent results on initial segments

doi:10.2178/bsl/1046288724
fatcat:rrfet36v4ngvrjsrkwv3r4i3le
*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*. ...##
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Page 23 of Mathematical Reviews Vol. , Issue 98A
[page]

1998
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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. ...##
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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. ...##
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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 ...##
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Page 5341 of Mathematical Reviews Vol. , Issue 92j
[page]

1992
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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 ...##
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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. ...##
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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. ...##
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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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