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Simple and immune relations on countable structures
2003
Archive for Mathematical Logic
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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
2004
Algebra and Logic
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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
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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
1986
Theoretical Computer Science
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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
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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
1988
Theoretical Computer Science
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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
2006
Bulletin of Symbolic Logic
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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]
2008
arXiv
pre-print
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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
1987
Journal of Philosophical Logic
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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
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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
2021
Soft Computing - A Fusion of Foundations, Methodologies and Applications
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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
2003
Annals of Pure and Applied Logic
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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
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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
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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
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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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