Given a set of propositions, one can consider its inconsistency hypergraph. Then the safisfiability of sets of clauses with respect to that hypergraph (see [2], [4]) turns out to be the usual satisfiability. The problem is which hypergraphs can be obtained from sets of formulas as inconsistency hypergraphs. In the present paper it is shown that this can be done for all hypergraphs with countabl...

This note contains a Stone-style representation theorem for compact Haus-dorff spaces. The note is very much inspired by some existing representation theorems and is expository in nature. The first representation theorem is by Jung and Sünderhauf in [JS] and there is also a version of it for compact Hausdorff spaces noted by D. Moshier [Mo], the ideas of which were described to us by A. Jung. T...

We introduce a set of transformations on the set of all probability distributions over a finite state space, and show that these transformations are the only ones that preserve certain elementary probabilistic relationships. This result provides a new perspective on a variety of probabilistic inference problems in which invariance considerations play a role. Two particular applications we consi...

Let (μn : n ≥ 0) be Borel probabilities on a metric space S such that μn → μ0 weakly. Say that Skorohod representation holds if, on some probability space, there are S-valued random variables Xn satisfying Xn ∼ μn for all n and Xn → X0 in probability. By Skorohod’s theorem, Skorohod representation holds (with Xn → X0 almost uniformly) if μ0 is separable. Two results are proved in this paper. Fi...

The articles [11], [7], [13], [1], [14], [5], [6], [4], [9], [10], [15], [16], [12], [2], [3], and [8] provide the notation and terminology for this paper. Let us note that every lower bound lattice which is Heyting is also implicative and every lattice which is implicative is also upper-bounded. In the sequel T denotes a topological space and A, B denote subsets of the carrier of T . The follo...

We present a constructive proof of the Stone-Yosida representation theorem for Riesz spaces motivated by considerations from formal topology. This theorem is used to derive a representation theorem for f-algebras. In turn, this theorem implies the Gelfand representation theorem for C*-algebras of operators on Hilbert spaces as formulated by Bishop and Bridges. Our proof is shorter, clearer, and...

The existence of admissible vectors for a locally compact group is closely related to the group's profile. In the compact groups, according to Peter-weyl theorem, every irreducible representation has admissible vector. In this paper, the conditions under which the inverse of this case is being investigated has been investigated. Conditions such as views that are admissible and stable will get c...

Introduction – Study of an Elementary Proof 1 1. The Lemmas of Thue and Vinogradov 4 2. Preliminaries on Quadratic Reciprocity and Quadratic Forms 4 2.1. Quadratic reciprocity law 4 2.2. Binary quadratic forms 5 3. Thue-Vinogradov Applied to Binary Quadratic Forms 7 4. First Applications of Theorem 9 8 4.1. Indefinite forms 8 4.2. Positive definite forms 10 5. Primes of the form x +Dy for idone...