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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.  ... 

The undecidability of the lattice of R.E. closed subsets of an effective topological space

Sheryl Silibovsky Brady, Jeffrey B. Remmel
1987 Annals of Pure and Applied Logic  
The first-order theory 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  ... 
doi:10.1016/0168-0072(87)90063-7 fatcat:6qmjevefb5fl3bsrrp7gj7shte

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  ... 

Some undecidability results for lattices in recursion theory

Jeffrey Carroll
1986 Pacific Journal of Mathematics  
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  ...  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.  ... 
doi:10.2140/pjm.1986.122.319 fatcat:nhhb3yhvyjdfpmm5b4rq2h2iu4

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.  ... 

Coding true arithmetic in the Medvedev degrees of Π10 classes

Paul Shafer
2012 Annals of Pure and Applied Logic  
Our coding 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.  ... 
doi:10.1016/j.apal.2011.10.002 fatcat:bjlbwdhrd5gelkxjyc4ftvlvuy

Degree Structures: Local and Global Investigations

Richard A. Shore
2006 Bulletin of Symbolic Logic  
Institutionally, it was an honor to serve as President 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.)  ... 
doi:10.2178/bsl/1154698739 fatcat:ct6b4ko77zhyfctmtfooxbk4ua

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.  ... 

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].  ... 

Master index to volumes 41-50

1990 Annals of Pure and Applied Logic  
., Intervals 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  ... 
doi:10.1016/0168-0072(90)90061-6 fatcat:inapyhmvyffpzkhhdq4qje4ahi

The Recursively Enumerable Degrees [chapter]

Richard A. Shore
1999 Studies in Logic and the Foundations of Mathematics  
(A sublattice 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 .  ... 
doi:10.1016/s0049-237x(99)80022-6 fatcat:yviyyg7uhfbolegitvgof4ga7m

Action Logic is Undecidable [article]

Stepan Kuznetsov
2019 arXiv   pre-print
We also prove the same complexity results for all recursively enumerable logics between action logic 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.  ... 
arXiv:1912.11273v1 fatcat:3fcadczxtvdkxoufcj3jfy2txq

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  ... 

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 — fL,); (ii) X, € L, and L,-card(X,,) < 6 for n € w, L, = U,,X,,; (iii) 8 is a regular cardinal in L,. (3)  ... 

Strong reducibilities

Piergiorgio Odifreddi
1981 Bulletin of the American Mathematical Society  
The theories 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  ... 
doi:10.1090/s0273-0979-1981-14863-1 fatcat:qbyl6mci6rd7jbxfwqjfmkit34
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