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  1. Joseph Barback (2006). On Hyper‐Torre Isols. Mathematical Logic Quarterly 52 (4):359-361.
    In this paper we present a contribution to a classical result of E. Ellentuck in the theory of regressive isols. E. Ellentuck introduced the concept of a hyper-torre isol, established their existence for regressive isols, and then proved that associated with these isols a special kind of semi-ring of isols is a model of the true universal-recursive statements of arithmetic. This result took on an added significance when it was later shown that for regressive isols, the property of being hyper-torre (...)
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  2. Joseph Barback (2005). Corrigendum to “Regressive Isols and Comparability”. Mathematical Logic Quarterly 51 (6):643-643.
    We give a correction to the paper [1] mentioned in the title.
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  3. Joseph Barback (1998). A Fine Structure in the Theory of Isols. Mathematical Logic Quarterly 44 (2):229-264.
    In this paper we introduce a collection of isols having some interesting properties. Imagine a collection W of regressive isols with the following features: u, v ϵ W implies that u ⩽ v or v ⩽ u, u ⩽ v and v ϵ W imply u ϵ W, W contains ℕ = {0,1,2,…} and some infinite isols, and u eϵ W, u infinite, and u + v regressive imply u + v ϵ W. That such a collection W exists is (...)
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  4. Joseph Barback (1997). On Regressive Isols and Comparability of Summands and a Theorem of R. Downey. Mathematical Logic Quarterly 43 (1):83-91.
    In this paper we present a collection of results related to the comparability of summands property of regressive isols. We show that if an infinite regressive isol has comparability of summands, then every predecessor of the isol has a weak comparability of summands property. Recently R. Downey proved that there exist regressive isols that are both hyper-torre and cosimple. There is a surprisingly close connection between non-recursive recursively enumerable sets and particular retraceable sets and regressive isols. We apply the theorem (...)
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  5. Joseph Barback (1994). Torre Models in the Isols. Journal of Symbolic Logic 59 (1):140-150.
    In [14] J. Hirschfeld established the close connection of models of the true AE sentences of Peano Arithmetic and homomorphic images of the semiring of recursive functions. This fragment of Arithmetic includes most of the familiar results of classical number theory. There are two nice ways that such models appear in the isols. One way was introduced by A. Nerode in [20] and is referred to in the literature as Nerode Semirings. The other way is called a tame model. It (...)
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  6. Joseph Barback (1988). On Infinite Series of Infinite Isols. Journal of Symbolic Logic 53 (2):443-462.
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  7. Joseph Barback (1976). Regressive Isols and Comparability. Mathematical Logic Quarterly 22 (1):403-412.
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  8. Joseph Barback (1972). Review: Erik Ellentuck, Solution of a Problem of R. Friedberg. [REVIEW] Journal of Symbolic Logic 37 (3):611-612.
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  9. Joseph Barback (1966). A Note on Regressive Isols. Notre Dame Journal of Formal Logic 7 (2):203-205.
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