We examine the reverse mathematical strength of a variation Hindman’s Theorem (HT) constructed by essentially combining HT with Thin Set to obtain principle that we call thin-HT. This states every coloring c:N→N has an infinite set S⊆N whose finite sums are thin for c, meaning there is i c(s)≠i all nonempty s finitely many distinct elements S. show computable instance thin-HT such solution comp...

According to Mack a space is countably paracompact if and only if its product with [0, 1] is δ-normal, i.e. any two disjoint closed sets, one of which is a regular Gδ-set, can be separated. In studying monotone versions of countable paracompactness, one is naturally led to consider various monotone versions of δ-normality. Such properties are the subject of this paper. We look at how these prop...

Recent work has shown that if an isostatic bar and joint framework possesses non-trivial symmetries, then it must satisfy some very simply stated restrictions on the number of joints and bars that are ‘fixed’ by various symmetry operations of the framework. For the group C3 which describes 3-fold rotational symmetry in the plane, we verify the conjecture proposed in [4] that these restrictions ...

We show that restricting a number of characterizations of the complexity class P to be positive (in natural ways) results in the same class of (monotone) problems which we denote by posP. By a well-known result of Razborov, posP is a proper subclass of the class of monotone problems in P. We exhibit complete problems for posP via weak logical reductions, as we do for other logically defined cla...

This paper proposes an extension of the multiversion two phase locking protocol, called EMV2PL, which enables update transactions to use versions while guaranteeing the serializability of all transactions. The use of the protocol is restricted to transactions, called write-then-read transactions that consist of two consecutive parts: a write part containing both read and write operations in som...