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Simple and immune relations on countable structures

2003
*
Archive for Mathematical Logic
*

Let A be a computable

doi:10.1007/s00153-002-0150-2
fatcat:x5yv2erhpvgtjpv5tvixqhkbwi
*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. ...##
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Relatively Hyperimmune Relations on Structures

2004
*
Algebra and Logic
*

Let R be a

doi:10.1023/b:allo.0000020846.55332.2f
fatcat:363ho5rpcveb3c5bww7f5qun3e
*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*. ...##
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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*). ...##
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A classification of complexity core lattices

1986
*
Theoretical Computer Science
*

A is 'almost P-

doi:10.1016/0304-3975(86)90140-4
fatcat:ax5zuhgutzellhieh2rmax2qwy
*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. ...##
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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. ...##
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The structure of generalized complexity cores

1988
*
Theoretical Computer Science
*

The

doi:10.1016/0304-3975(88)90119-3
fatcat:rhahfnfwxbhwhcwofywsgyu2tu
*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. ...##
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Classification from a Computable Viewpoint

2006
*
Bulletin of Symbolic Logic
*

We give sample

doi:10.2178/bsl/1146620059
fatcat:efmtdpvde5e2tic5t4wunr4mbu
*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 ...##
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Classification from a Computable Viewpoint
[article]

2008
*
arXiv
*
pre-print

In the present paper, we describe some recent work

arXiv:0803.3293v1
fatcat:v64gbjnw4jghreao7w4nszzlxu
*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*. ...##
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Skolem's paradox and constructivism

1987
*
Journal of Philosophical Logic
*

That draft did not contain Charles McCarty's results (Sections 7

doi:10.1007/bf00257838
fatcat:gctyqs27sjfdjjwlaf7nv6syfy
*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. ...##
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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

2021
*
Soft Computing - A Fusion of Foundations, Methodologies and Applications
*

AbstractIt is introduced an

doi:10.1007/s00500-021-05955-3
fatcat:l7yomupmfrbzhj73njfeijuz7u
*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. ...##
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Turing degrees of hypersimple relations on computable structures

2003
*
Annals of Pure and Applied Logic
*

Let A be an inÿnite computable

doi:10.1016/s0168-0072(02)00113-6
fatcat:qpxvvq65ybbt5a76hmoeqdh2ua
*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*. ...##
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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). ...##
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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*...##
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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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