Skolem Research Articles

Further Results on Near Skolem Difference Mean Graphs

Further Results on Near Skolem Difference Mean Graphs

Skolem Difference Mean Graphs

Skolem difference mean labelings of some predefined graphs are studied.

Geraldine Brady. From Peirce to Skolem. A neglected chapter in the history of logic. Elsevier, Amsterdam, 2000, xi + 468 pp.

Geraldine Brady. From Peirce to Skolem. A neglected chapter in the history of logic. Elsevier, Amsterdam, 2000, xi + 468 pp.

Perfect Skolem sets

A Skolem sequence is a sequence s 1 , s 2 , … , s 2 n (where s i ∈ A = { 1 , … , n } ) , each s i occurs exactly twice in the sequence and the two occurrences are exactly s i positions apart. A set A that can be used to construct Skolem sequences is called a Skolem set. The problem of deciding which sets of the form A = { 1 , … , n } are Skolem sets was solved by Thoralf Skolem in the late 1950s. We study the natural generalization where A is allowed to be any set of n positive integers. We give necessary conditions for the existence of Skolem sets of this generalized form. We conjecture these necessary conditions to be sufficient, and give computational evidence in favor of our conjecture. We investigate special cases of the conjecture and prove that the conjecture holds for some of them. We also study enumerative questions and show that this problem has strong connections with problems related to permutation displacements.

Deflating skolem

Deflating skolem

Book Review: Geraldine Brady. From Peirce to Skolem: A Neglected Chapter in the History of Logic

Book Review: Geraldine Brady. From Peirce to Skolem: A Neglected Chapter in the History of Logic

Parametrizing SL2(Z) and a question of Skolem

Parametrizing SL2(Z) and a question of Skolem

Recursive functionals and quantifiers of finite types revisited. V

Publisher Summary In the eighteen years since my last visit to Oslo, I have cherished a very pleasant recollection of an evening spent in the home of Thoralf Skolem. I am glad that the younger Norwegian logicians are keeping up the tradition so brilliantly started by him investigators from all parts have been pursuing higher and generalized recursion theory while I have been looking away. Also I am pleased to observe how many able In the theory developed in my original papers (1959 and 1963) on the subject I a m revisiting, there is a partial recursive function ϕ(σ2,a) such that ϕ(λτ1 θ,a,τ1),a) to avoid this anomaly was not then pursued in depth is a partial recursive function of a for no completely defined (1963 LVI p. 110). A suggestion there (p.111) for extending the theory Platek in 1966 (to which my attention was drawn by Gandy 1967 p. 239) used my 1963 p. 110 example to show that the first recursion theorem (Kleene I M 1952a p. 348) does not hold in my 1959, 1963 theory ( as Ialsodidin 1963 LXVIpp. 120, 125). Platek developed a theory avoiding these anomalies by using what the called hereditarily consistent functionals. The present treatment (which for me is a resurrection of my 1963 p. 111 suggestion) gives the first recursion theorem a central role thinking along these lines before encountering Gandy 1967 and Platek 1966 exact relationship of the present treatment to Platek's and other work since 1963 remains to be clarified.

Skolem fragments.

Skolem fragments.

On a problem of Th. Skolem.

On a problem of Th. Skolem.

Skolem's Promises and Paradoxes

Skolem's Promises and Paradoxes

Word Problems and Recursively Enumerable Degrees of Unsolvability. A Sequel on Finitely Presented Groups

The present paper is a sequel to [B4.2 We specify an explicit grouptheoretic construction based on techniques of Britton [D] which, if added to the Thue system constructions of [B], results in the exhibition of a finitely presented group with word problem of arbitrary recursively enumerable degree of unsolvability. One may be given the arbitrary degree as the word problem of a given Thue system. Only the results of [B] are needed, not the details, except for two definitions of notation.3 The exhibition of a finitely generated, recursively related group of arbitrary recursively enumerable degree of unsolvability (as described in [B3])2 is briefly noted. Related independent lines of development are the announcements by Cejtin [B9] (for Thue systems), and by Fridman [B13] (for finitely presented groups), as well as the detailed arguments by Clapham [Bl0] (for finitely presented groups), and by Shepherdson [B251 (for Thue systems). (See footnote 6.) Like [BI, this work is dedicated to the memory of Thoralf Skolem.

Obituary of Thoralf A. Skolem.

Obituary of Thoralf A. Skolem.

Verification of a Conjecture of Th. Skolem.

Verification of a Conjecture of Th. Skolem.