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Simple and immune relations on countable structures

Sergei. S. Goncharov, Valentina. S. Harizanov, Julia. F. Knight, Charles F. D. McCoy
2003 Archive for Mathematical Logic  
Let A be a computable structure and let R be a new relation on its domain.  ...  We also establish, under certain effectiveness conditions on A and R, a necessary and sufficient condition for the existence of a computable copy B of A in which the image of R (¬R, resp.) is simple (immune  ...  (ii) A new relation on a countable structure B is simple relative to B if it is c.e. relative to B and its complement is immune relative to B.  ... 
doi:10.1007/s00153-002-0150-2 fatcat:x5yv2erhpvgtjpv5tvixqhkbwi

Relatively Hyperimmune Relations on Structures

S. S. Goncharov, C. F. McCoy, J. F. Knight, V. S. Harizanov
2004 Algebra and Logic  
Let R be a relation on the domain of a computable structure A.  ...  h-simple (formally h-immune, resp.) on A.  ...  Introduction We consider only countable structures for computable relational languages, and investigate relatively hyperimmune and relatively hypersimple relations on these structures.  ... 
doi:10.1023/b:allo.0000020846.55332.2f fatcat:363ho5rpcveb3c5bww7f5qun3e

Page 4 of Mathematical Reviews Vol. , Issue 2004g [page]

2004 Mathematical Reviews  
D. (1-WI: Madison, WI Simple and immune relations on countable structures. (English summary) Arch. Math. Logic 42 (2003), no. 3, 279-291. Let be a countable structure and let R be a relation on it.  ...  For the case of a computable structure ./, under an extra condition, they prove criteria for the existence of an isomorphic copy of .¥ in which the image of R is simple (immune).  ... 

A classification of complexity core lattices

Pekka Orponen
1986 Theoretical Computer Science  
A is 'almost P-immune' or not.  ...  We study the structure of this lattice, proving that, surprisingly, there are only three possibilities: assuming the lattice is not trivial (which happens if A is in P), its shape depends only on whether  ...  Lemma 3.2 was first observed by Isfikowitz, and the characterization of the lattice in Corgllary 4.2 is due to Du.  ... 
doi:10.1016/0304-3975(86)90140-4 fatcat:ax5zuhgutzellhieh2rmax2qwy

Page 624 of Mathematical Reviews Vol. , Issue 92b [page]

1992 Mathematical Reviews  
The author formulates the results in terms of a so-called structural pre-order, i.e., the set of countable models of the theory that is pre-ordered by the relation of elementary embedding. O. V.  ...  With a recursive set that is bi-immune for P, one can associate a nontrivial 1-cheatable set polynomially m-reducible to it.  ... 

The structure of generalized complexity cores

Ronald V. Book, Ding-Zhu Du
1988 Theoretical Computer Science  
The structure of the lattice of hard cores of A with respect to C depends only on the relationship between A and C If A is finite or in C, then the lattice is the trivial one-point lattice.  ...  The setting involves a countable class C of sets of strings that is closed under finite union and under finite variation. For any set A let C" denote the collection of all C E C such that C E A.  ...  be a class of sets and let ity, and levelability In this section w investigate the properties of "immunity" and "levelability" of sets and relate t to the notions of hard core.  ... 
doi:10.1016/0304-3975(88)90119-3 fatcat:rhahfnfwxbhwhcwofywsgyu2tu

Classification from a Computable Viewpoint

Wesley Calvert, Julia F. Knight
2006 Bulletin of Symbolic Logic  
We give sample structure and non-structure theorems based on the complexity of the isomorphism relation, and on Borel embeddings. Section 2 gives some background on computable structures.  ...  Section 3 describes results on the isomorphism relation for a number of mathematically interesting classes—various kinds of groups and fields.  ...  There is a family of 2 ℵ0 pairwise bi-immune sets. 2 . 2 (≤ a ) a∈P are reflexive, transitive binary relations on tuples from the structures A a 3. the relations have the back-and-forth property; i.e  ... 
doi:10.2178/bsl/1146620059 fatcat:efmtdpvde5e2tic5t4wunr4mbu

Classification from a Computable Viewpoint [article]

Wesley Calvert, Julia F. Knight
2008 arXiv   pre-print
In the present paper, we describe some recent work on classification in computable structure theory.  ...  In model theory and descriptive set theory, there is a large body of work, showing that certain classes of mathematical structures admit classification, while others do not.  ...  We give sample structure and non-structure theorems based on the complexity of the isomorphism relation, and on Borel embeddings. Section 2 gives some background on computable structures.  ... 
arXiv:0803.3293v1 fatcat:v64gbjnw4jghreao7w4nszzlxu

Skolem's paradox and constructivism

Charles McCarty, Neil Tennant
1987 Journal of Philosophical Logic  
That draft did not contain Charles McCarty's results (Sections 7 and 8) on the independence of versions of the countable models theorem from extensions of intuitionistic set theory.  ...  As Timothy Smiley has observed, Keisler's completeness proof for a (classical) logic based on a simple set of axioms and rules for this quantifier gives an intriguingly quick answer to the question whether  ...  ' Here is the best behaved countable fragment of the real epsilon relation that one can get.  ... 
doi:10.1007/bf00257838 fatcat:gctyqs27sjfdjjwlaf7nv6syfy

Page 5094 of Mathematical Reviews Vol. , Issue 93i [page]

1993 Mathematical Reviews  
Summary: “For a finite alphabet & we define a binary relation on 2=" x 2°, called balanced immunity.  ...  We give a general method to find a balanced immune set B for any countable class # and prove that, for s(n) = o(t(n)) and t(n) > n, there is a B € SPACE(t(n)), which is balanced immune for SPACE(s(n)),  ... 

Dynamic Łukasiewicz logic and its application to immune system

Antonio Di Nola, Revaz Grigolia, Nunu Mitskevich, Gaetano Vitale
2021 Soft Computing - A Fusion of Foundations, Methodologies and Applications  
AbstractIt is introduced an immune dynamic n-valued Łukasiewicz logic $$ID{\L }_n$$ I D Ł n on the base of n-valued Łukasiewicz logic $${\L }_n$$ Ł n and corresponding to it immune dynamic $$MV_n$$ M V  ...  Kripke semantics is developed for immune dynamic Łukasiewicz logic $$ID{\L }_n$$ I D Ł n with application in immune system.  ...  It means that by Kripke frame we capture just the relational structure of an immune system.  ... 
doi:10.1007/s00500-021-05955-3 fatcat:l7yomupmfrbzhj73njfeijuz7u

Turing degrees of hypersimple relations on computable structures

Valentina S. Harizanov
2003 Annals of Pure and Applied Logic  
Let A be an inÿnite computable structure, and let R be an additional computable relation on its domain A.  ...  certain e ective sequences of relations on A.  ...  In [5] , we investigated immunity and simplicity of relations on computable structures, and relative immunity and relative simplicity of relations on countable structures.  ... 
doi:10.1016/s0168-0072(02)00113-6 fatcat:qpxvvq65ybbt5a76hmoeqdh2ua

Page 4719 of Mathematical Reviews Vol. , Issue 87i [page]

1987 Mathematical Reviews  
Symbolic Logic 51 (1986), no. 2, 412-420. 87i:03067 The author introduces a new notion (he calls it almost decid- ability) that approximates decidability with respect to countable structures.  ...  T is said to be locally p-No-categorical if for all finite A and countable models M and N of T, Ba(M) is isomorphic to Ba(N).  ... 

Page 34 of Mathematical Reviews Vol. , Issue 92a [page]

1992 Mathematical Reviews  
respect to some polynomi- ally related ordering <) and M accepts if and only if at least one oracle query is answered affirmatively.  ...  Completeness is shown using normal forms, from which we also obtain very simple proofs of previously known properties of these logics, such as decidability, interpolation, and a theorem of Vaananen on  ... 

Page 2257 of Mathematical Reviews Vol. , Issue 85f [page]

1985 Mathematical Reviews  
Wainer (Leeds) Li, Xiang 85f:03039 Effective immune sets, program index sets and effectively simple sets—generalizations and applications of the recursion theorem.  ...  If one is content to interpret ZFC~ +V = HC in Ag, then these trees can be taken as relations on w, i.e. ®(z) is N(z); this is Example 3.12.  ... 
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