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Embedding jump upper semilattices into the Turing degrees

2003
*
Journal of Symbolic Logic (JSL)
*

we call

doi:10.2178/jsl/1058448451
fatcat:lvp5qgexibezvhzanwolzybwvm
*jump*, and is*the*jusl of*Turing**degrees*. ... We prove that every countable*jump**upper**semilattice*can be*embedded*in , where a*jump**upper**semilattice*(jusl) is an*upper**semilattice*endowed with a strictly increasing and monotone unary operator that ... Observe that, D = D, ≤ T , ∨, ,*the*set of*Turing**degrees*together with*the**Turing*reduction,*the*join operation and*the**Turing**Jump*is a jusl. ...##
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Page 5961 of Mathematical Reviews Vol. , Issue 2004h
[page]

2004
*
Mathematical Reviews
*

5961 03D Computability and recursion theory
2004h:03089 03D28 03B25 03E5S0
Montalban, Antonio (1-CRNL; Ithaca, NY

*Embedding**jump**upper**semilattices**into**the**Turing**degrees*. (English summary) J. ... Let Z be a jusl of*Turing**degrees*.*The*author proves that every countable*upper**semilattice*can be*embedded*in Z. ...##
###
Density of a final segment of the truth-table degrees

1984
*
Pacific Journal of Mathematics
*

We give a simple and explicit example of elementary inequivalence of

doi:10.2140/pjm.1984.115.409
fatcat:h2pewm3ddvfcdivrhpb4djjpgm
*the**Turing**degrees*to*the*truth-table*degrees*. ... In constructing this example, we show that every truth-table*degree*above that of*the*halting problem is*the**jump*of another truth-table*degree*. ... A partial ordering is an*upper**semilattice*if finite supremums are always defined. An*upper**semilattice*JSf is homogeneous if any*embedding**into*<£? ...##
###
Page 6761 of Mathematical Reviews Vol. , Issue 87m
[page]

1987
*
Mathematical Reviews
*

There is a natural

*embedding*of*the*(total)*Turing**degrees**into**the*partial*degrees*, and hence*into**the*enumeration*degrees*(e-*degrees*), these being notational variants of*the*partial*degrees*as defined ... Finally, paralleling Sacks’s*jump*theorem for r.e.*Turing*de- grees,*the*author shows that*the**jumps*of*the*I,*degrees*are ex- actly*the*Ilz*degrees*> 0’. ...##
###
An extension of the recursively enumerable Turing degrees

2007
*
Journal of the London Mathematical Society
*

Consider

doi:10.1112/jlms/jdl015
fatcat:gggbcm5sffb23axocnoioragmm
*the*countable*semilattice*RT consisting of*the*recursively enumerable*Turing**degrees*. ... We exhibit a natural*embedding*of RT*into*Pw which is one-toone, preserves*the**semilattice*structure of RT , carries 0 to 0, and carries 0 ′ to 1. ...*Embedding*R T*into*P w In this section we exhibit a specific, natural*embedding*of*the*countable*upper**semilattice*R T*into**the*countable distributive lattice P w . Definition 5.1. ...##
###
A note on continuities of the poset of Turing degrees

2014
*
International Journal of Contemporary Mathematical Sciences
*

In this note, continuities of

doi:10.12988/ijcms.2014.4777
fatcat:7ot4pjkfn5fsnlq7wk6qudy2sa
*the*poset of*Turing**degrees*are considered. ... ideal completion of D, and thus is an algebraic lattice; (4) D can be*embedded**into*an algebraic lattice as an*embedded*base. ... Consequently, D can be*embedded**into**the*algebraic lattice as an*embedded*base. ...##
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Page 1314 of Mathematical Reviews Vol. 50, Issue 5
[page]

1975
*
Mathematical Reviews
*

*The*question on p. 309, line 12 has subsequently been answered by Lachlan and Lebeuf; every countable

*upper*

*semilattice*can be

*embedded*as an initial segment of

*the*

*degrees*. ... In

*the*present paper

*the*author studies similar questions for

*the*

*upper*

*semilattices*L(S) of classes of equivalent numerations for nontrivial sets S and

*the*

*upper*

*semilattices*L. ...

##
###
Local Initial Segments of The Turing Degrees

2003
*
Bulletin of Symbolic Logic
*

AbstractRecent results on initial segments of

doi:10.2178/bsl/1046288724
fatcat:rrfet36v4ngvrjsrkwv3r4i3le
*the**Turing**degrees*are presented, and some conjectures about initial segments that have implications for*the*existence of nontrivial automorphisms of*the**Turing*...*degrees*are indicated. ... This article concerns*the*algebraic study of*the**upper**semilattice*of*Turing**degrees*. ...##
###
Page 6520 of Mathematical Reviews Vol. , Issue 93m
[page]

1993
*
Mathematical Reviews
*

First it is shown that

*the*non-p-generic*degrees*are dense in R (*the**upper**semilattice*of r.e.*degrees*). ... in*the*r.e.*degrees*, P’ is order-*embedded*in*the**degrees*r.e. in and above 0’, these*embeddings*preserve least and greatest elements, and f corresponds to*the*operation under these*embeddings*. ...##
###
SOME FUNDAMENTAL ISSUES CONCERNING DEGREES OF UNSOLVABILITY
[chapter]

2008
*
Computational Prospects of Infinity
*

Motivation Recall that D T is

doi:10.1142/9789812796554_0017
fatcat:p2ovjhh4lrefbabj4we22svqlq
*the**upper**semilattice*consisting of all*Turing**degrees*. ... Note that R T ,*the**upper**semilattice*of recursively enumerable*Turing**degrees*, is*embedded*in P w . Moreover, 0 ′ and 0 are*the*top and bottom elements of both R T and P w . ...##
###
JSL volume 68 issue 3 Cover and Front matter

2003
*
Journal of Symbolic Logic (JSL)
*

MIRAGLIA : 946 A hierarchy for

doi:10.1017/s0022481200008458
fatcat:s5wpgx2x5rarxiw52kt4h3iuq4
*the*plus cupping*Turing**degrees*, by YONG WANG and ANGSHENG LI 972*Embedding**jump**upper**semilattices**into**the**Turing**degrees*, by ANTONIO MONTALBAN 989 Classical and constructive ...*The*BULLETIN and*the*JOURNAL are*the*official organs of*the*Association for Symbolic Logic, an international organization for furthering research in symbolic logic and*the*exchange of ideas among mathematicians ...##
###
A Rigid Cone in the Truth-Table Degrees with Jump
[chapter]

2016
*
Lecture Notes in Computer Science
*

*The*automorphism group of

*the*truth-table

*degrees*with order and

*jump*is fixed on

*the*set of

*degrees*above

*the*fourth

*jump*, 0 (4) . ... At separate stages of

*the*preparation of this article

*the*author was supported by a Marie Curie Fellowship of

*the*European Community Programme "Improving Human Potential" under contract number HPMF-CT- ...

*The*following lemma will have many applications: Lemma 5.7. Let U ⊆ ω. Acknowledgments We thank Noam Greenberg for a correction to an early draft of this article. ...

##
###
A rigid cone in the truth-table degrees with jump
[article]

2010
*
arXiv
*
pre-print

*The*automorphism group of

*the*truth-table

*degrees*with order and

*jump*is fixed on

*the*set of

*degrees*above

*the*fourth

*jump*of 0. ... This material is based upon work supported by

*the*National Science Foundation under Grants No. 0652669 and 0901020. ... It is not known whether

*the*structure of

*the*

*Turing*

*degrees*is rigid, but it is known [JS] that

*the*structure of

*the*

*Turing*

*degrees*with

*jump*contains a rigid cone. ...

##
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Intervals Without Critical Triples
[chapter]

1998
*
Logic Colloquium '95
*

This paper is concerned with

doi:10.1007/978-3-662-22108-2_2
dblp:conf/logicColl/CholakDS95
fatcat:bq2bw4kibbaxhitnoaekqludge
*the*construction of intervals of computably enumerable*degrees*in which*the*lattice M 5 (see Figure 1 ) cannot be*embedded*. ... Actually, w e construct intervals I of computably enumerable*degrees*without any w eak critical triples (this implies that M 5 cannot be*embedded*in I, see Section 2). ... Let a, b 0 and b 1 be elements in any*upper**semilattice*L (such as*the**Turing**degrees*or*the*computably enumerable*Turing**degrees*). ...##
###
Intermediate logics and factors of the Medvedev lattice
[article]

2006
*
arXiv
*
pre-print

We investigate

arXiv:math/0606494v1
fatcat:3spff4xw3vae5ikudiveba77qy
*the*initial segments of*the*Medvedev lattice as Brouwer algebras, and study*the*propositional logics connected to them. ... In our case it suffices to embed F ω as an initial*upper**semilattice*of*the**Turing**degrees*. Notice that*the*range of such an*embedding*consists of Muchnik*degrees*. ... U embeds*into*Fr × (U) as an*upper**semilattice*, and for every distributive lattice L, if f : U −→ L is a homomorphism of*upper**semilattices*, then*the**embedding*of U*into*Fr × (U) extends to a unique lattice ...
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