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### PRIORITY ARGUMENTS VIA TRUE STAGES

ANTONIO MONTALBÁN
2014 Journal of Symbolic Logic (JSL)
Apparent 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.  ...

### The undecidability of the recursively enumerable degrees

Leo Harrington, Saharon Shelah
1982 Bulletin of the American Mathematical Society
The lemma is proven, of course, by a 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.  ...

### On the existence of a strong minimal pair [article]

George Barmpalias and Mingzhong Cai and Steffen Lempp and Theodore A. Slaman
2016 arXiv   pre-print
Now in the following 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  ...

### Anti-Molinism is Undefeated!

2000 Faith and Philosophy
So if (4) is 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.  ...

### On the existence of a strong minimal pair

George Barmpalias, Mingzhong Cai, Steffen Lempp, Theodore A. Slaman
2015 Journal of Mathematical Logic
Now in the following 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.  ...

### Bounding computably enumerable degrees in the Ershov hierarchy

Angsheng Li, Guohua Wu, Yue Yang
2006 Annals of Pure and Applied Logic
If not, then define δ s = δ s−1 and go to the next 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.  ...

### The recursively enumerable α-degrees are dense

Richard A. Shore
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.  ...

### Computably enumerable sets and quasi-reducibility

R. Downey, G. LaForte, A. Nies
1998 Annals of Pure and Applied Logic
If C ≤ Q A 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 .  ...

### Guidelines for the Analysis and Design of Argumentation-based Recommendation Systems

Mario Leiva, Maximiliano C. D. Budan, Gerardo I. Simari
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.  ...

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

Jonathan Tallant, Sam Baron
2018 Synthese
In this paper we offer a response to one 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.  ...

### Embedding the Diamond Lattice in the c.e. tt-Degrees with Superhigh Atoms [chapter]

Douglas Cenzer, Johanna N. Y. Franklin, Jiang Liu, Guohua Wu
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.  ...

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

Douglas Cenzer, Johanna N. Y. Franklin, Jiang Liu, Guohua Wu
2010 Archive for Mathematical Logic
Jockusch and Mohrherr's construction involves only a finite injury 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.  ...

### Decidability and Invariant Classes for Degree Structures

Manuel Lerman, Richard A. Shore
1988 Transactions of the American Mathematical Society
For the sake of a contradiction, suppose that 8 is the node on the 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.  ...

### Decidability and invariant classes for degree structures

Manuel Lerman, Richard A. Shore
1988 Transactions of the American Mathematical Society
For the sake of a contradiction, suppose that 8 is the node on the 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.  ...

### Oracle-dependent properties of the lattice of NP sets

Steven Homer, Wolfgang Maass
1983 Theoretical Computer Science
The constructions of the oracles are finite injury 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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