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A Friedberg enumeration of equivalence structures

2017
*
Journal of Mathematical Logic
*

We also prove that there exists an e↵ective

doi:10.1142/s0219061317500088
fatcat:zhvnxrd5jve3roofqu42sfx4lm
*Friedberg**enumeration**of*all isomorphism types*of*infinite computable*equivalence**structures*. ... More specifically, we produce an e↵ective*Friedberg*(i.e., injective)*enumeration**of*computable*equivalence**structures*, up to isomorphism. ... There exists*a**Friedberg**enumeration**of*the class*of*computable*equivalence**structures*, up to isomorphism. ...##
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Intrinsic bounds on complexity and definability at limit levels

2009
*
Journal of Symbolic Logic (JSL)
*

We show that for every computable limit ordinal α, there is

doi:10.2178/jsl/1245158098
fatcat:swighvldknbpjnouhuj6ys2t4e
*a*computable*structure*that is categorical, but not relatively categorical (*equivalently*, it does not have*a*formally Scott family). ... We also show that for every computable limit ordinal α, there is*a*computable*structure*with an additional relation R that is intrinsically on , but not relatively intrinsically on (*equivalently*, it is ... S has*a*unique anti-*Friedberg*ω-f -*enumeration*, up to strong ∆ 0 ω -*equivalence*. Proof. We construct an anti-*Friedberg*ω-f -*enumeration*G*of**a*family S. ...##
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Page 4 of Mathematical Reviews Vol. , Issue 81K
[page]

1981
*
Mathematical Reviews
*

An

*enumeration*y is*a*Gédel num- bering if y satisfies the*enumeration*and s-m-n theorems and y is*a**Friedberg*numbering if is one-to-one. (R. M.*Friedberg*con- structed*a**Friedberg*numbering [J. ... Regarding homo- geneity it is shown (Theorem 5.8) that if the ordering*of*degrees with*a*parameter for 0 is elementarily*equivalent*to the ordering*of*degrees >b with*a*corresponding parameter for b’, ...##
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Comparing Classes of Finite Structures

2004
*
Algebra and Logic
*

Then (

doi:10.1023/b:allo.0000048827.30718.2c
fatcat:x3rzqjvvfjdi7nu7fz6iqoaxzi
*A*n ) n∈ω is an infinite computable*Friedberg**enumeration**of**a*subclass*of*K. Now, suppose that(*A*n ) n∈ω is an infinite computable*Friedberg**enumeration**of**a*subclass*of*K. ... There is*a*class*of*finite*structures*K that has*a*computable*enumeration*but no computable*Friedberg**enumeration*. Proof. We want to create*a*class K with*a*computable*enumeration*E. ...##
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Comparing Classes of Finite Structures
[article]

2008
*
arXiv
*
pre-print

We introduce

arXiv:0803.3291v1
fatcat:xxrl4kc5hnd43hn66zgh5knneu
*a*reducibility on classes*of**structures*, essentially*a*uniform*enumeration*reducibility. ... The class*of*cyclic graphs and the class*of*finite prime fields are*equivalent*, and are properly below the class*of*arbitrary finite graphs. ... Then (*A*n ) n∈ω is an infinite computable*Friedberg**enumeration**of**a*subclass*of*K. Now, suppose that(*A*n ) n∈ω is an infinite computable*Friedberg**enumeration**of**a*subclass*of*K. ...##
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Calibrating Computational Complexity via Definability: The Work of Julia F. Knight

2022
*
Notices of the American Mathematical Society
*

Determining whether the class

doi:10.1090/noti2436
fatcat:6g2qjctksnd7plspwz7ysetjpa
*of**equivalence**structures*has*a*computable*Friedberg**enumeration*proved challenging. ... However, Goncharov and Knight's conjecture was false-Downey, Melnikov, and Ng provided*a**Friedberg**enumeration**of*all*equivalence**structures*in 2017. ...##
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Page 4405 of Mathematical Reviews Vol. , Issue 2001G
[page]

2001
*
Mathematical Reviews
*

Call

*a*pair*of*computably*enumerable*(c.e.) sets (Ap,*A*))*a**Friedberg*splitting*of**a*c.e. set*A*if*A*is the disjoint union*of*Ao and*A*}, and for any c.e. set B, if Ag B or*A*; MB is complemented in the ...*A*congruence relation on the lattice*of*c.e. sets is an*equivalence*relation on # such that union and intersection are well defined on the*equivalence*classes. ...##
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Page 31 of Mathematical Reviews Vol. 58, Issue 1
[page]

1979
*
Mathematical Reviews
*

Post’s problem about the existence

*of*T-incomparable recursively*enumerable*sets was solved by R.*Friedberg*and*A*. Muénik by another method. ... From the introduction: “We fix*a*recursively*enumerable*(r.e.) field F with recursive*structure*, and let U be the vector space over F consisting*of*the ultimately vanishing elements*of*F° with the usual ...##
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Page 2284 of Mathematical Reviews Vol. , Issue 86f
[page]

1986
*
Mathematical Reviews
*

*of*recursively

*enumerable*sets (pp. 21-32); Richard

*A*. ... Kechris, Determinacy and the

*structure*

*of*L(R) (pp. 271- 283); Alain Louveau, Recursivity and capacity theory (pp. 285- 301); Donald

*A*. ...

##
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JSL volume 67 issue 2 Cover and Front matter

2002
*
Journal of Symbolic Logic (JSL)
*

on computable

doi:10.1017/s0022481200009555
fatcat:jledthgadjenrmxcg6vxfdb4le
*structures*in the presence*of**A*-J isomorphisms, by DENIS R. ... FERNANDES and FERNANDO On orbits, pf prompt and low computably*enumerable*sets, by KEVIN WALD . 649 Definable incompleteness and*Friedberg*splittings, by RUSSELL MILLER 679 Degree spectra*of*relations ...##
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Isomorphisms of splits of computably enumerable sets

2003
*
Journal of Symbolic Logic (JSL)
*

We show that if

doi:10.2178/jsl/1058448453
fatcat:toj3wyhit5earei7woorv242be
*A*and are automorphic via Φ then the*structures*(*A*) and () are Δ3 0-isomorphic via an isomorphism Ψ induced by Φ. ... Then we use this result to classify completely the orbits*of*hhsimple sets. ... Introduction We will work in the*structure**of*the computably*enumerable*sets. The language is just inclusion, ⊆. This*structure*is called E. Our understanding*of*automorphisms*of*E is unique to E. ...##
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Page 1844 of Mathematical Reviews Vol. , Issue 94d
[page]

1994
*
Mathematical Reviews
*

944:03082
94d:03082 03D25 Downey, Rod (NZ-VCTR; Wellington); Stob, Michael (1-CLVN; Grand Rapids, MI)

*Friedberg*splittings*of*recursively*enumerable*sets. ...*A*splitting*A*; U A2 =*A**of*an r.e. set*A*is called*a**Friedberg*(or f-) splitting if for any r.e. set W with W \*A*notr.e., W. Aj #2 for i= 1,2. ...##
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Algebraic aspects of the computably enumerable degrees

1995
*
Proceedings of the National Academy of Sciences of the United States of America
*

*A*set

*A*

*of*nonnegative integers is computably

*enumerable*(c.e.), also called recursively

*enumerable*(r.e.), if there is

*a*computable method to list its elements. ... The class

*of*sets B which contain the same information as

*A*under Turing computability (<T) is the (Turing) degree ofA, and

*a*degree is c.e. if it contains

*a*c.e. set. ... These results demonstrated that 2R has

*a*more complicated global

*structure*than anticipated by the results

*of*the 1960s. ...

##
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Friedberg numberings in the Ershov hierarchy

2014
*
Archive for Mathematical Logic
*

We show that for every n ≥ 1, there exists

doi:10.1007/s00153-014-0402-y
fatcat:52zsc6vsevgmxcaeaguogpmzqq
*a*Σ −1 n -computable family which up to*equivalence*has exactly one*Friedberg*numbering which does not induce the least element*of*the corresponding Rogers semilattice ... Rogers semilattice R i*a*(*A*)*of**a*family*A*⊆ Σ i*a*is*a*quotient*structure**of*all Σ i*a*-computable numberings*of*the family*A*modulo*equivalence**of*the numberings ordered by the relation induced by reducibility ... For every k, if π k is*a**Friedberg*numbering*of**A*then g k is*a*total function and g k reduces π k to α. Proof. Suppose that π k is*a**Friedberg*numbering*of**A*. ...##
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Page 3557 of Mathematical Reviews Vol. , Issue 83i
[page]

1983
*
Mathematical Reviews
*

For the

*structures*, he describes the closure*of*R under elementary*equivalence*, and the notions*of*projective relation (ARB then means that*A*and B are interpreted in*a*certain way within the same*structure*... s book [Theory*of*recursive functions and effective computability, McGraw-Hill, New York, 1967; MR 37 #61] for basic terminology). In 1956, R. M.*Friedberg*and*A*.*A*. ...
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