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Page 648 of Mathematical Reviews Vol. , Issue 88b
[page]

1988
*
Mathematical Reviews
*

(NZ-VCTR)

*Undecidability**of**L*(*F*.,.)*and**other**lattices**of**r.e*.*substructures*. Ann. Pure Appl. Logic 32 (1986), no. 1, 17-26. ... The author obtains a general result on*undecidability*which implies the*undecidability**of*the theory*of*the*lattice**of**r.e*.*substructures**of*a number*of*important recursive structures. ...##
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The undecidability of the lattice of R.E. closed subsets of an effective topological space

1987
*
Annals of Pure and Applied Logic
*

The first-order theory

doi:10.1016/0168-0072(87)90063-7
fatcat:6qmjevefb5fl3bsrrp7gj7shte
*of*the*lattice**of*recursively enumerable closed subsets*of*an effective topological space is proved*undecidable*using the undeeidability*of*the first-order theory*of*the*lattice*... In particular, the first-order theory*of*the*lattice**of*recursively enumerable closed subsets*of*Euclidean n-space, for all n, is*undecidable*. ... Introduction The study*of*the*lattices**of**r.e*.*substructures**of*a fixed recursively presented structure was introduced by Metakides*and*Nerode [13] ,*and**undecidability*results for such*lattices*in the ...##
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Page 3377 of Mathematical Reviews Vol. , Issue 88g
[page]

1988
*
Mathematical Reviews
*

The study

*of*the*lattice**of**r.e*.*substructures**of*a fixed recursively presented structure was introduced by Metakides*and*Nerode,*and**undecidability*results for such*lattices*in the realm*of*recursive ... It then follows from the*undecidability**of*the theory*of*the*lattice**of**r.e*. sets that the theory*of*the*lattice**of**r.e*. open subsets (*and*hence*r.e*. closed subsets)*of*an effective topological space is ...##
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Some undecidability results for lattices in recursion theory

1986
*
Pacific Journal of Mathematics
*

The

doi:10.2140/pjm.1986.122.319
fatcat:nhhb3yhvyjdfpmm5b4rq2h2iu4
*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 ... This paper presents two more*undecidability*results for*lattices**of**r.e*.*substructures*but no advanced recursion theoretic techniques will be required. ... Supply name*and*address*of*author to whom proofs should be sent. ...##
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Page 3553 of Mathematical Reviews Vol. , Issue 91G
[page]

1991
*
Mathematical Reviews
*

Arslanov (Kazan)
91g:03089 03D35 03D45
Downey, Rod (NZ-VCTR)
Correction to: “

*Undecidability**of**L*(*F*.,,.)*and**other**lattices**of**r.e*.*substructures*” [Ann. Pure Appl. ... From the text: “In the paper cited in the heading, we gave a proof that a wide class*of**lattices**of**r.e*.*substructures*had*undecidable*first-order theories. The proof consisted*of*two parts. ...##
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Coding true arithmetic in the Medvedev degrees of Π10 classes

2012
*
Annals of Pure and Applied Logic
*

Our coding

doi:10.1016/j.apal.2011.10.002
fatcat:bjlbwdhrd5gelkxjyc4ftvlvuy
*of*arithmetic in E s also shows that the Σ 0 3 -theory*of*E s as a*lattice**and*the Σ 0 4 -theory*of*E s as a partial order are*undecidable*. ... Finally, we show that the Σ 0 3 -theory*of*E w as a*lattice**and*the Σ 0 4 -theory*of*E w as a partial order are*undecidable*. 1 classes have been persistent objects*of*study throughout computability theory ... Shore for introducing me to the Medvedev degrees*and*Muchnik degrees*and*for many helpful discussions. Thanks also to my anonymous reviewers for their helpful comments. ...##
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Degree Structures: Local and Global Investigations

2006
*
Bulletin of Symbolic Logic
*

Institutionally, it was an honor to serve as President

doi:10.2178/bsl/1154698739
fatcat:ct6b4ko77zhyfctmtfooxbk4ua
*of*the Association*and*I want to thank my teachers*and*predecessors for guidance*and*advice*and*my fellow officers*and*our publisher for their work ... The occasion*of*a retiring presidential address seems like a time to look back, take stock*and*perhaps look ahead. ... -*r.e*. if there is such an*f*with the number*of*s with*f*(x; s) 6 =*f*(x; s + 1) bounded by a recursive function*of*n.) ...##
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Page 2272 of Mathematical Reviews Vol. , Issue 87e
[page]

1987
*
Mathematical Reviews
*

Finally, he proves that if B is an infinite recursive Boolean algebra, then the

*lattice**of**r.e*. subalgebras*of*B is*undecidable*. Decheng Ding (Nanjing) Golunkov, Yu. V. (2-KAZA); Savel’ev, A. ... . =, X} for X*r.e*., infinite*and*coinfinite”. The author shows that this set is*L*$-complete*and*so solves the problem. ...##
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Page 625 of Mathematical Reviews Vol. , Issue 96b
[page]

1996
*
Mathematical Reviews
*

. algebra @ with a Noetherian congruence

*lattice*such that the word problem on @ is*undecidable*. (3) Fi- nally, they construct a finitely generated*r.e*. perfect algebra with immune as well as nonimmune ... Here decidability*and*computability over an arbitrary ring are understood in the sense*of*[*L*. Blum, M. Shub*and*S. Smale, Bull. Amer. Math. Soc. (N.S.) 21 (1989), no. 1, 1-46; MR 90a:68022]. ...##
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Master index to volumes 41-50

1990
*
Annals of Pure and Applied Logic
*

., Intervals

doi:10.1016/0168-0072(90)90061-6
fatcat:inapyhmvyffpzkhhdq4qje4ahi
*and*sublattices*of*the*r.e*. weak truth table degrees, Part II: nonbounding 44 (1989) 153-172 Downey, R.G., Correction to "*Undecidability**of**L*(*F*,)*and**other**lattices**of**r.e*. ...*substructures*" (Corrigendum) 48 (1990) 299-301 Downey, R.G.,*Lattice*nonembeddings*and*initial segments*of*the recursively enumerable degrees 49 (1990) 97-119 Downey, R.G.*and*Remmel, J.B., Classification ...##
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The Recursively Enumerable Degrees
[chapter]

1999
*
Studies in Logic and the Foundations of Mathematics
*

(A sublattice

doi:10.1016/s0049-237x(99)80022-6
fatcat:yviyyg7uhfbolegitvgof4ga7m
*L**of*a*lattice**L*is generated by a subset A*of**L*if*L*is the smallest sublattice*of**L*containing A. ... If we consider the language*of*usls, then we must note that, in any usl*L*, the*substructure*generated by a finite set x 1 , ...x n is finite*and**of*size at most 2 n . ...##
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Action Logic is Undecidable
[article]

2019
*
arXiv
*
pre-print

We also prove the same complexity results for all recursively enumerable logics between action logic

arXiv:1912.11273v1
fatcat:3fcadczxtvdkxoufcj3jfy2txq
*and*infinitary action logic; for fragments*of*those only one*of*the two*lattice*(additive) connectives ... For a stronger system which uses an ω-rule instead (infinitary action logic) Buszkowski*and*Palka (2007) have proved Π_1^0-completeness (thus,*undecidability*). ... Being a Young Russian Mathematics award winner, the author thanks its jury*and*sponsors for this high honour. ...##
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Page 406 of Mathematical Reviews Vol. 49, Issue 2
[page]

1975
*
Mathematical Reviews
*

*and*the

*other*can be Ax.2=n for any n>0, or (he claims) Avx.7+t for any t20. ... They take Post’s 2313 | 07 LOGIC

*AND*FOUNDATIONS 4 | construction

*of*a hypersimple

*r.e*. set that is given relative beg to a fixed but arbitrary standard enumeration

*of*

*r.e*. sets, | ambec

*and*show that ...

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Page 606 of Mathematical Reviews Vol. , Issue 87b
[page]

1987
*
Mathematical Reviews
*

It turns out that the continuous

*r.e*. degrees form a distributive*lattice*within which the classical*r.e*. T-degrees (*of*type 1 objects) are embedded—though not as an elementary*substructure*. ...*and*there are 3 < @*and*a sequence (X,,:n < w) such that (i) (Vy < «)(Vf:7 — B)(*f*bounded —*f*€*L*,); (ii) X, €*L*,*and**L*,-card(X,,) < 6 for n € w,*L*, = U,,X,,; (iii) 8 is a regular cardinal in*L*,. (3) ...##
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Strong reducibilities

1981
*
Bulletin of the American Mathematical Society
*

The theories

doi:10.1090/s0273-0979-1981-14863-1
fatcat:qbyl6mci6rd7jbxfwqjfmkit34
*of*the orderings*of**r.e*. m-degrees*and**l*-degrees are*undecidable**and*nonaxiomatizable. Problem 22. Are the theories*of*the orderings*of**r.e*. /-degrees*and*T-degrees decidable? ... For a given (recursively presented) algebraic structure, the*lattice**of*the recursively enumerable*substructures**of*it can be considered,*and*a theory analogous to (but not consequence*of*) the one for ...
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