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PRIORITY ARGUMENTS VIA TRUE STAGES

2014
*
Journal of Symbolic Logic (JSL)
*

Apparent

doi:10.1017/jsl.2014.11
fatcat:7kjlyx4ujrg6vp7e2rzir6vxku
*true**stages*. As we know, a*true**stage*is one at which we are guessing a finite initial segment of 0 correctly. We will call them 1-*true**stages*. ... Let us remark that there are two other known general frameworks for*priority**arguments*: The workers method developed by Harrington [Har76, Har79] (see also Knight [Kni90a, Kni90b] ), and the iterated ... Let t j be as in the definition of ∇ ω t -*true**stages*(Definition 6.1, so t j is essentially the oracle-use of the computation ϕ Lemma 7.8. ...##
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The undecidability of the recursively enumerable degrees

1982
*
Bulletin of the American Mathematical Society
*

The lemma is proven, of course, by a

doi:10.1090/s0273-0979-1982-14970-9
fatcat:fwqu3iceq5dmtl47f3is5xrcdi
*priority**argument*. The type of*priority**argument*used can best be described as an infinite injury*argument*with a finite injury*priority**argument*on top of it. ... Thus for \Jj a sentence of the language of partial orderings: \p is*true*of some partial ordering iff (by the usual proof of the completeness theorem) P f= \p for some P recursive in 0' iff (by the lemma ... The type of*priority**argument*used can best be described as an infinite injury*argument*with a finite injury*priority**argument*on top of it. ...##
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On the existence of a strong minimal pair
[article]

2016
*
arXiv
*
pre-print

Now in the following

arXiv:1610.03591v1
fatcat:fhctld7ofveqjcokfzoy2zycdq
*arguments*, we always assume that we have a node ξ on the*true*path and we have passed the*stage*when all nodes to the left stop acting. ... Such a discussion may be beneficial to the reader who is familiar with these older and simpler*arguments*; but it may also be helpful to the reader who is not an expert in 0 ′′′ -*priority**arguments*and ...##
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Anti-Molinism is Undefeated!

2000
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Faith and Philosophy
*

So if (4) is

doi:10.5840/faithphil20001715
fatcat:nv6wp56benduppqdddazt2ul6y
*true*[i.e., if explanatory*priority*is transitive], we must conclude that 5*. The truth of (A*) is explanatorily prior to our children's coming to love God. ... II As we have seen, Craig's central objection to Adams'*argument*is that the notion of explanatory*priority*is equivocal. ...##
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On the existence of a strong minimal pair

2015
*
Journal of Mathematical Logic
*

Now in the following

doi:10.1142/s0219061315500038
fatcat:wexdqlencfd3baupkvc7bemeu4
*arguments*, we always assume that we have a node ξ on the*true*path and we have passed the*stage*when all nodes to the left stop acting. ... At A-*stages*, the*argument*is much trickier, but is very similar to the standard*argument*used in the style of Lachlan's gap/co-gap construction. ...##
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Bounding computably enumerable degrees in the Ershov hierarchy

2006
*
Annals of Pure and Applied Logic
*

If not, then define δ s = δ s−1 and go to the next

doi:10.1016/j.apal.2005.10.004
fatcat:as3psv42jjakrbrhdetdqetwt4
*stage*. Otherwise, choose β as the one with the highest*priority*waiting for an A-permission and execute the disagreement*argument*as follows: 1. ... If β has executed the disagreement*argument*after*stage*s β , then define δ s (t) = d. 2. ... By the choice of s 0 , no higher*priority*strategy can initialize β after*stage*s 2 , and so β is satisfied*via*this inequality, and never acts afterwards. (1) holds. ...##
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The recursively enumerable α-degrees are dense

1976
*
Annals of Mathematical Logic
*

*Priority*

*arguments*are undoubtedly the hallmark of recursion theory. ... As a beginning, the simplest type of

*priority*

*argument*was used by Sacks in his construction of two incomparable meta-r.e, degrees [ 151. ...

*Priority*

*arguments*are undoubtedly the hallmark of recursion theory. ...

##
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Computably enumerable sets and quasi-reducibility

1998
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Annals of Pure and Applied Logic
*

If C ≤ Q A

doi:10.1016/s0168-0072(98)00013-x
fatcat:3biois4ic5ep5bza6q2pjdh32m
*via*φ a , then at any A-*true**stage*, if φ a (y) and y ∈ C, then W φa(y) ↾ a s ⊆ A s . ... Again, we must use the*true**stage*method to guarantee enough expansionary*stages*. ... Recall D i,j,e is G i ≤ Q G j*via*Φ e . We intend to satisfy this requirement in the usual way by diagonalization, picking a new follower x u [s] after each initialization of R u . ...##
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Guidelines for the Analysis and Design of Argumentation-based Recommendation Systems

2020
*
IEEE Intelligent Systems
*

*Argumentation*-based tools offer the possibility of analyzing complex and dynamic domains by generating and analyzing

*arguments*for and against recommending a specific item based on the users' preferences ...

*Priorities*: We use "better rule(rule1, rule2)" to encode that R1 has

*priority*over R2. ... Step 2: Establish

*priorities*We consider that the preference criterion that best responds to this particular domain is rule

*priority*. ...

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It's one thing to rule them all and another thing to bind them

2018
*
Synthese
*

In this paper we offer a response to one

doi:10.1007/s11229-018-01983-z
fatcat:xf5pxjamzba4tguu7dpkxrae3i
*argument*in favour of*Priority*Monism, what Jonathan Schaffer calls the nomic*argument*for monism. We proceed in three*stages*. ... We begin by introducing Jonathan Schaffer's*Priority*Monism and the nomic*argument*for that view. ... (Schaffer 2013: p. 72) Call this: the nomic*argument*for*Priority*Monism. The nomic*argument*forges a critical connection between substance-hood and evolving*via*the fundamental laws. ...##
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Embedding the Diamond Lattice in the c.e. tt-Degrees with Superhigh Atoms
[chapter]

2009
*
Lecture Notes in Computer Science
*

*priority*lower than α after the last α-expansionary

*stage*. ... Jockusch and Mohrherr's construction involves only a finite injury

*argument*, while ours involves an infinite injury

*argument*, which is necessary to make A and B superhigh. ...

##
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A superhigh diamond in the c.e. tt-degrees

2010
*
Archive for Mathematical Logic
*

Jockusch and Mohrherr's construction involves only a finite injury

doi:10.1007/s00153-010-0198-3
fatcat:jex2uj4exvarhhssbrv6za6zau
*argument*, while ours involves an infinite injury*argument*. This is necessary to make A and B superhigh. ... If (1) is*true*, then we enumerate k s , 0 into A. If (1) is not*true*but (2) is, then we enumerate k s , 0 into B. ...##
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Decidability and Invariant Classes for Degree Structures

1988
*
Transactions of the American Mathematical Society
*

For the sake of a contradiction, suppose that 8 is the node on the

doi:10.2307/2000985
fatcat:u4axyuwf5vcwpo3gn54exu4yii
*true*path below a of lowest*priority*which exercises control over y*via*infinitely many t. ... A D-*true**stage*s is one for which Vr. > s(d(t) > d(s)). There are infinitely many D-*true**stages*and as usual if s is one and $S(D3; x) = i then $(D; x) = i and so AjtS is an initial segment of Aj. ...##
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Decidability and invariant classes for degree structures

1988
*
Transactions of the American Mathematical Society
*

For the sake of a contradiction, suppose that 8 is the node on the

doi:10.1090/s0002-9947-1988-0973174-0
fatcat:kzehuldwhrezxp6jxcctwh7sue
*true*path below a of lowest*priority*which exercises control over y*via*infinitely many t. ... A D-*true**stage*s is one for which Vr. > s(d(t) > d(s)). There are infinitely many D-*true**stages*and as usual if s is one and $S(D3; x) = i then $(D; x) = i and so AjtS is an initial segment of Aj. ...##
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Oracle-dependent properties of the lattice of NP sets

1983
*
Theoretical Computer Science
*

The constructions of the oracles are finite injury

doi:10.1016/0304-3975(83)90003-8
fatcat:6xjze2fr4zaqjjpwiywdwivfxy
*priority**arguments*. ... We construct several oracles, all of which make P# NP, and which in addition make the above-mentioned statements either*true*or false. ... The constructions are (with the exception of Theorem 3.1) finite injury*priority**arguments*. ...
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