We investigate combinatorial lowness properties of sets of natural numbers (reals). The real A is super-low if A′ ≤tt ∅′, and A is jump-traceable if the values of {e}A(e) can be effectively approximated in a sense to be specified. We investigate those properties, in particular showing that super-lowness and jump-traceability coincide within the r.e. sets but none of the properties implies the o...

After everyone has voted, the votes in each ballot position are counted, and the winner of each race is declared. Barring the use of some form of ranked-preference ballot, the algorithms required are hardly more than mere summations. What makes elections difficult is the problem of performing this summation over a canvassing hierarchy spanning many polling places and local election offices, whe...

1. Introduction What is true and what is not depends upon how the world is: that there are no white ravens is true because there are no white ravens. That much, Trenton Merricks accepts. But he denies that principles about truthmaking can do any heavy lifting in metaphysics, and he provides powerful, sophisticated arguments for this denial. The hunt for individual truthmakers for specific truth...

This paper deals with topologically trivial Legendrian knots in tight and overtwisted contact 3-manifolds. The first parts (Sections 1-3) contain a thorough exposition of the proof of the classification of topologically trivial Legendrian knots (i.e. Legendrian knots bounding embedded 2-disks) in tight contact 3-manifolds (Theorem 1.7), and, in particular, in the standard contact S. These parts...

Coset enumeration, based on the methods described by Todd & Coxeter, is one of the basic tools for investigating nitely presented groups. The process is not well understood, and various pathological presentations of, for example, the trivial group have been suggested as challenge problems. Here we consider one such presentation. We show that it is much easier than it rst appears, albeit at the ...

It is show to be consistent that there is a non-trivial autohomeomorphism of βN \ N while all such autohomeomorphisms are trivial on some open set. The model used is one due to Velickovic in which, coincidentally, Martin’s Axiom also holds.

We present a very simple, cryptographic, Byzantine-agreement protocol that, with n = 3t + 1 players, t of which are malicious, halts in expected 9 rounds.